Grade 10 Circles. | Mathematics | Page 1

gritty sundial Jun 9, 2023, 2:11 PM

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So in the picture P,Q,R,S are points on a circle centred at O and <PSQ = 130°.
Find <PRQ, <POQ, , <OPQ

(Idk what category this belongs to)

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someone help i got a whole worksheet to complete rn 🥲

stoic canopy Jun 9, 2023, 2:14 PM

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Circle theorems will be of great help here, example:

gritty sundial Jun 9, 2023, 2:14 PM

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PQRS is a cyclic quadrilateral

gritty sundial Jun 9, 2023, 2:15 PM

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gritty sundial PQRS is a cyclic quadrilateral

@gritty sundial

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All the edges of the quadrilateral are touching the circle

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Sum of opposite angles of a cyclic quadrilateral is 180°

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so <PRQ will be 180-130?

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Yup

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okay so <POQ?

gritty sundial Jun 9, 2023, 2:17 PM

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stoic canopy Circle theorems will be of great help here, example:

This

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Angle subtended by a chord/arc at the centre is double the angle subtended by it at any other point on the circle

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Oh so

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2x50

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or 2x <PRQ

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how am i gonna find <OPQ tho

halcyon trail Jun 9, 2023, 2:25 PM

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note that OP and OQ are radii of the circle

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therefore OPQ is isoceles, with <OPQ = <OQP

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we already know one angle

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and what the angles in a trangle add up to

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so just solve

gritty sundial Jun 9, 2023, 2:27 PM

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ie

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50°?

halcyon trail Jun 9, 2023, 2:27 PM

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no?

gritty sundial Jun 9, 2023, 2:27 PM

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ok wait

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40?

halcyon trail Jun 9, 2023, 2:29 PM

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yes

gritty sundial Jun 9, 2023, 2:29 PM

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YESS

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ty

gritty sundial Jun 9, 2023, 2:30 PM

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gritty sundial ty

The property of isosceles triangle and the property of cyclic quadrilateral and the angle at the centre theorem are very useful, so just keep them handy

gritty sundial Jun 9, 2023, 2:31 PM

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gritty sundial The property of isosceles triangle and the property of cyclic quadrilateral and ...

Thanks for the reminder

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ok

amber obsidianBOT Jun 9, 2023, 2:31 PM

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@burnt ocean has given 1 rep to @surreal parrot

gritty sundial Jun 9, 2023, 2:31 PM

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how do i give the other guy rep

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wtvr

gritty sundial Jun 9, 2023, 2:33 PM

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gritty sundial how do i give the other guy rep

Ping and say thanks

amber obsidianBOT Jun 9, 2023, 2:34 PM

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@surreal parrot has given 1 rep to @burnt ocean

gritty sundial Jun 9, 2023, 2:47 PM

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@halcyon trail thanks

amber obsidianBOT Jun 9, 2023, 2:47 PM

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@burnt ocean has given 1 rep to @halcyon trail

gritty sundial Jun 9, 2023, 2:48 PM

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another question idk if i can ask here

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but

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does 100 and 999 leave remainder 2 when divided by 7?

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does not have to be the last division

halcyon trail Jun 9, 2023, 2:49 PM

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find the least multiple less than that

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if you want you can also use modulus properties to get the remainder

gritty sundial Jun 9, 2023, 2:50 PM

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it has to be a 3 digit number

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999÷7 = 142 with a reminder of 5

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999-5 is the biggest 5 digit number divisible by 7

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994

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@gritty sundial

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no like

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999÷7

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gives 2

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wait

halcyon trail Jun 9, 2023, 2:52 PM

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wdym gives 2

gritty sundial Jun 9, 2023, 2:53 PM

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there's one 7 in 9

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so

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9-7

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2

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like that

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U don't see the last digit only

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U see the number as a whole

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4 isn't divisible by 7 but 14 is

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nono

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the question isnt check if its divisible or not

halcyon trail Jun 9, 2023, 2:54 PM

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can you send a screenshot of the problem

gritty sundial Jun 9, 2023, 2:54 PM

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Yeah

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I'll type it instead

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That'll work

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Consider the sequence of three digits numbers which leaves a remainder 2 on division by 7.
a) Find first term
b) Find last term

halcyon trail Jun 9, 2023, 2:56 PM

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oh

gritty sundial Jun 9, 2023, 2:56 PM

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arithmetic sequence

halcyon trail Jun 9, 2023, 2:57 PM

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well 999 = 5 (mod 7)

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so 2 (mod 7) = 5 - 3 ( mod 7)

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or 999 - 3

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so 996

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996 = 2 (mod 7)

gritty sundial Jun 9, 2023, 2:58 PM

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First term = 100
Last term= 996

halcyon trail Jun 9, 2023, 2:59 PM

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102 leaves remainder of 4

gritty sundial Jun 9, 2023, 2:59 PM

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Wait yeah

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ye

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first term is 100

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and last term is 996

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thanks again @halcyon trail @gritty sundial

#Grade 10 Circles.