Geometry thales theorem | Mathematics | Page 1

gleaming ravenBOT May 28, 2023, 10:20 AM

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proven trench May 28, 2023, 10:21 AM

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How do i solve ex

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4

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Part A

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tropic beacon May 28, 2023, 10:36 AM

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Hi

proven trench May 28, 2023, 10:36 AM

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Hi

tropic beacon May 28, 2023, 10:36 AM

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Do u see that OF = OE?

proven trench May 28, 2023, 10:37 AM

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Yes

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Radii in same circle

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They're both 3 cm

tropic beacon May 28, 2023, 10:37 AM

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So it comes to proving OA=OI

tropic beacon May 28, 2023, 10:37 AM

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tropic beacon So it comes to proving OA=OI

Yes?

proven trench May 28, 2023, 10:37 AM

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OI is 5cm

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OOOOOHOOOO

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Now i knowit

tropic beacon May 28, 2023, 10:38 AM

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Great

proven trench May 28, 2023, 10:38 AM

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Since EF//AI

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So we can apple thales

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So

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Apply*

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Then:

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OF/OI=OE/OA

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Now we replace

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3/OI=3/5

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Now

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3x5/3=OI

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So

tropic beacon May 28, 2023, 10:39 AM

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Yuss

proven trench May 28, 2023, 10:39 AM

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OI=5

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Tysm

tropic beacon May 28, 2023, 10:40 AM

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Congrats

tropic beacon May 28, 2023, 10:40 AM

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proven trench Tysm

I didn't even do anything lol

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bhappy

proven trench May 28, 2023, 10:40 AM

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U showed me how to think

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I didnt know where to start

tropic beacon May 28, 2023, 10:40 AM

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Ur welcome if

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Ig

proven trench May 28, 2023, 10:40 AM

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Ty

tropic beacon May 28, 2023, 10:40 AM

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happy

proven trench May 28, 2023, 10:45 AM

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@tropic beacon

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Pls help again

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In number 5 a

tropic beacon May 28, 2023, 10:46 AM

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U see how AFO is a right angle

proven trench May 28, 2023, 10:46 AM

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Yes

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OOOOH

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So that means

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FI is a diameters

tropic beacon May 28, 2023, 10:46 AM

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What

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No

proven trench May 28, 2023, 10:46 AM

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And same with FEI

tropic beacon May 28, 2023, 10:46 AM

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FI isn't diameter

proven trench May 28, 2023, 10:46 AM

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I mean in C'

tropic beacon May 28, 2023, 10:47 AM

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?

proven trench May 28, 2023, 10:47 AM

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Read question again

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They want in circle C'

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Oh wait

tropic beacon May 28, 2023, 10:47 AM

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No. OA is 5, OF is 3, so by pythagoras, AF is 4

proven trench May 28, 2023, 10:47 AM

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AI is diameter

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Not FI

tropic beacon May 28, 2023, 10:47 AM

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What

proven trench May 28, 2023, 10:48 AM

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Yes bro

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Because

tropic beacon May 28, 2023, 10:48 AM

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BE is diameter

proven trench May 28, 2023, 10:48 AM

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I mean in circle C'

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Yes i know its not drawn

tropic beacon May 28, 2023, 10:48 AM

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Ahhh

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Ok

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Yes

proven trench May 28, 2023, 10:48 AM

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But we have to imagine it

tropic beacon May 28, 2023, 10:49 AM

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But u need not use that for verifying AF=4

proven trench May 28, 2023, 10:49 AM

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tropic beacon May 28, 2023, 10:49 AM

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U just wanna find AF right?

proven trench May 28, 2023, 10:49 AM

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tropic beacon But u need not use that for verifying AF=4

Why do we care about AF

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Nooooo

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I said question 5 a

tropic beacon May 28, 2023, 10:49 AM

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Ohh

proven trench May 28, 2023, 10:49 AM

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Not b

tropic beacon May 28, 2023, 10:49 AM

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Oh I saw b

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Wait

proven trench May 28, 2023, 10:49 AM

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Its ok

tropic beacon May 28, 2023, 10:50 AM

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Ok that's easy

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AFO and AEI are right angles

proven trench May 28, 2023, 10:50 AM

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Is it like i said diameter??

tropic beacon May 28, 2023, 10:50 AM

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U know how two lines from end point of diameter to the circumference make a right angle?

proven trench May 28, 2023, 10:50 AM

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Yes

tropic beacon May 28, 2023, 10:50 AM

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So u can assume AI to be diameter

proven trench May 28, 2023, 10:50 AM

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Yes

tropic beacon May 28, 2023, 10:50 AM

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Yes

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U got it

proven trench May 28, 2023, 10:51 AM

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But how are they on same circle

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Oh wait

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Nvm

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Ok

tropic beacon May 28, 2023, 10:51 AM

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Yes

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Nice

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U can solve bro

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Good luck

proven trench May 28, 2023, 10:51 AM

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And then we find AF with Pythagoras

tropic beacon May 28, 2023, 10:51 AM

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Yes

proven trench May 28, 2023, 10:51 AM

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Like u said

tropic beacon May 28, 2023, 10:51 AM

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Yea

proven trench May 28, 2023, 10:51 AM

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And in 5C

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Diameter

tropic beacon May 28, 2023, 10:51 AM

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No wait

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Sorry

proven trench May 28, 2023, 10:51 AM

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Is AI

tropic beacon May 28, 2023, 10:51 AM

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Wait

proven trench May 28, 2023, 10:52 AM

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What

tropic beacon May 28, 2023, 10:52 AM

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We haven't yet verifed

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Why it has to be

proven trench May 28, 2023, 10:52 AM

#

tropic beacon May 28, 2023, 10:52 AM

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On a circle

proven trench May 28, 2023, 10:52 AM

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Oh

tropic beacon May 28, 2023, 10:52 AM

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Frankly idk

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Someone else might help

proven trench May 28, 2023, 10:52 AM

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Isnt it because

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AI is diameter and F is a point on circle

tropic beacon May 28, 2023, 10:53 AM

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Ive done this stuff like 4 years ago

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Never touched again

proven trench May 28, 2023, 10:53 AM

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proven trench AI is diameter and F is a point on circle

And same with the other point

tropic beacon May 28, 2023, 10:53 AM

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_<

proven trench May 28, 2023, 10:53 AM

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Its ok i knew it

tropic beacon May 28, 2023, 10:53 AM

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proven trench And same with the other point

I don't think it's sufficient proof

proven trench May 28, 2023, 10:53 AM

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But how

tropic beacon May 28, 2023, 10:54 AM

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Wiat u can do one thing

proven trench May 28, 2023, 10:54 AM

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Since the anglea are right

tropic beacon May 28, 2023, 10:54 AM

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Construct a mid point M of AI

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Oh wait yes

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Ok maybe what i said earlier was right

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If its right angle

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It has to lie on the circle with AI diameter

proven trench May 28, 2023, 10:54 AM

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Yrs

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Yes

tropic beacon May 28, 2023, 10:55 AM

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But I think it's better if u

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Verify with someone else

proven trench May 28, 2023, 10:55 AM

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Ok

tropic beacon May 28, 2023, 10:55 AM

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Cuz I'm too rusty with this studf

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Hello Rusty, Im Dad

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bhappy

proven trench May 28, 2023, 10:55 AM

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And 5 c is

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Because

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AI is diameter

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Umm

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We use Pythagoras

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So

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AF2 + FI2= AI2

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So

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Wait what

tropic beacon May 28, 2023, 10:57 AM

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Is the Triangle Right Angled tho?

proven trench May 28, 2023, 10:57 AM

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Yes

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How do we solve 5 b

tropic beacon May 28, 2023, 10:59 AM

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Give me a sec

proven trench May 28, 2023, 10:59 AM

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Ok

tropic beacon May 28, 2023, 11:03 AM

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proven trench AF2 + FI2= AI2

Yeah this

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Pythagoras

proven trench May 28, 2023, 11:04 AM

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But we dont have AI

tropic beacon May 28, 2023, 11:05 AM

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AO^2= AF^2+OF^2

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Still a right angle Triangle

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All good?

proven trench May 28, 2023, 11:06 AM

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We dont have AO

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Oh nvm

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Its 5

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Ok so then

tropic beacon May 28, 2023, 11:07 AM

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.-.

proven trench May 28, 2023, 11:07 AM

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25=af2 +9

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AF2=-25+9

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What

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How

tropic beacon May 28, 2023, 11:08 AM

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-AF^2=-25+9

proven trench May 28, 2023, 11:08 AM

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Man math aint mathing

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Oh

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Yes

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-AF2=-16

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AF2=16

tropic beacon May 28, 2023, 11:09 AM

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4

proven trench May 28, 2023, 11:09 AM

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AF=4

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Ok

tropic beacon May 28, 2023, 11:09 AM

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K

proven trench May 28, 2023, 11:09 AM

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Now

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We find AI

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tropic beacon May 28, 2023, 11:10 AM

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proven trench AF2 + FI2= AI2

This

proven trench May 28, 2023, 11:10 AM

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man we dont have FI

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Ohhh

tropic beacon May 28, 2023, 11:11 AM

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FO+OI

proven trench May 28, 2023, 11:11 AM

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We dont have OI

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Oh wait

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We use thales theorem

tropic beacon May 28, 2023, 11:11 AM

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4 b)????

proven trench May 28, 2023, 11:12 AM

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wdym

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We found AF

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Its 4

tropic beacon May 28, 2023, 11:12 AM

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You already t
Found OI at 4.b)

tropic beacon May 28, 2023, 11:12 AM

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proven trench

Read it

proven trench May 28, 2023, 11:13 AM

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Oh

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So

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Its

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8

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So

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AI2=64+16

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AI2=80

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AI=square root 80

tropic beacon May 28, 2023, 11:14 AM

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$4 \sqrt(5)$

weary roostBOT May 28, 2023, 11:14 AM

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I have No User Name but I must

proven trench May 28, 2023, 11:14 AM

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Yes

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But wait

tropic beacon May 28, 2023, 11:15 AM

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...

proven trench May 28, 2023, 11:15 AM

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There was another way

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Faster way

tropic beacon May 28, 2023, 11:15 AM

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Ok...

proven trench May 28, 2023, 11:15 AM

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Using thales theorem

tropic beacon May 28, 2023, 11:15 AM

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I'm gonna leave

proven trench May 28, 2023, 11:16 AM

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Since OF/OI=OE/OA=FE/AI

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Then

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We replace values

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3/5=3/5=FE/AI

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Now

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Hmmm

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Nvm

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It wont work

#Geometry thales theorem