Circle theorems

[ember sorrel]

Help me please

[silent burrow]

Which one are you having trouble with?

[golden bramble]

god these figures cant even afford centers for the circles duh

[ember sorrel]

sadly all of them 😭

I already have the answer for 11,12,13 and 14 but not 15 and the rest

[golden bramble]

use similar triangles

and circle theorems yes yes

[ember sorrel]

huh

[golden bramble]

construct more line segments

😎

[silent burrow]

Tell me the relations between these two lines

[ember sorrel]

I have no idea

[silent burrow]

Ok have you studied these circle theorems?

[ember sorrel]

No sir

Cus I don't understand at all

[golden bramble]

wheres the center of the circle

[silent burrow]

We don't have to know the center, M is not the center btw

[ember sorrel]

Oh

[golden bramble]

if you have the center and you can determine the distance between the center and the 2 chords then yes

[golden bramble]

then i have no clue

looks like cd is longer

than ab

[ember sorrel]

But how does problem 15 work? Cuz like there's an x and y

[silent burrow]

Alright, I'm not gonna prove how they have been found ( or if you want I can show you)

[silent burrow]

I will tell you

[golden bramble]

similar triangles

[ember sorrel]

eh

[golden bramble]

or just ask alieeen

he seems enthusiastic

[ember sorrel]

oh

[golden bramble]

but use similar triangles and the circle theorems

and use tangent lines

i have this kind of homework as well

just that i dont find x and y

[ember sorrel]

i don't understand how

[golden bramble]

same 😎

[silent burrow]

Look at this once more

[golden bramble]

whats special about this?

just a circle with 2 silly chords

[ember sorrel]

uhm

I'm confuse

[silent burrow]

Look at this formula

[golden bramble]

oh right similar triangles

[silent burrow]

This is the relation between two lines

[ember sorrel]

yeah

oh okok

[golden bramble]

ah right

how do i

forget

about this

duh

[silent burrow]

Using the formula j just sent

Now tell me the value of CM

[ember sorrel]

i don't know..

[golden bramble]

omg yeah this is too difficult

😭😭

[golden bramble]

1

[silent burrow]

Look at this

[ember sorrel]

oh

[golden bramble]

i see, so this formula derived from using similar triangles

[silent burrow]

AM×MB = CM × MD

[golden bramble]

new knowledge

[silent burrow]

Cuh please let me tell him how we found the answer for sec sorry

[golden bramble]

alr

sorry

[silent burrow]

Ok look

[ember sorrel]

oh how tho

[silent burrow]

We said that
AM × MB = CM × MD

Do you agree?

[ember sorrel]

Yes sir

[silent burrow]

Alright now according to the thing I sent,
AM=5
MB=2
MD=10

The only thing missing is CM

[ember sorrel]

yeah

[silent burrow]

Now can you plug in the values and find CM please?

[ember sorrel]

I'm sorry how do I do that

[golden bramble]

💀

[silent burrow]

Imagine CM as x

Now just say:
AM × MB = CM × MD

plug in the values:

5 × 2 = x × 10

[ember sorrel]

ok and then

[silent burrow]

Cuh you can speak now sorry for holding you back 😅

[silent burrow]

Now divide by 10 to isolate x

[golden bramble]

i suppose you all know about circle theorems yes?

[silent burrow]

I know them yes

[ember sorrel]

oh so 10 ÷ 10 = 1?

Mkaaayy

[silent burrow]

Yep exactly

[golden bramble]

OMG BRO FIGURED OUT

😎😎😎😎

[ember sorrel]

oh

[golden bramble]

what a genius

bravo

[silent burrow]

Alright now I'm giving you guys one more example

[ember sorrel]

mkay

[golden bramble]

i feel like i have to give yall in depth explanations

you cant just use this formula damn 😭

alright im waiting for the new example

[silent burrow]

You were right, the formula comes from triangle similarities

Now tell me the value of x

[ember sorrel]

hmm

[silent burrow]

Step by step do the things we did in the previous example

[ember sorrel]

2?

[silent burrow]

Yez!

[golden bramble]

nailed it buddy

[ember sorrel]

Yeyyy 🥳

[golden bramble]

im proud of you bro

😭😭

[ember sorrel]

ty ty

It's an achievement

[golden bramble]

youre making me tear up

[silent burrow]

Alright now let's make it a little bit harder

[ember sorrel]

Yes sir

[silent burrow]

Find the value of x

[ember sorrel]

Oh my

[silent burrow]

I also want you to answer this one

It's not hard I swear

Just multiply and you will see

[golden bramble]

jesus christ university level math

lord have mercy on me

x = 2

[silent burrow]

Yez

[golden bramble]

😎

[silent burrow]

What have you done so far?

[ember sorrel]

I'm still solving sir

[silent burrow]

Btw don't call me sir I'm just a student 😭

[golden bramble]

also you gotta consider the case where ab and cd are secants, nof just chords

[ember sorrel]

I have no idea

[golden bramble]

how was thy day my good sir

[silent burrow]

Always remember the formula
AM × MB = CM × MD

now just plug in values

[ember sorrel]

Okok

[silent burrow]

2 × (x + 1) = x × 3

Please solve the equation

[ember sorrel]

Ok

[silent burrow]

2x + 2 = 3x

[ember sorrel]

2x + 2 = 3x
2x = 3x
2/ 3 ?

it's wrong isn't it

[silent burrow]

It is

Imagine you had this equation

[ember sorrel]

dang

[silent burrow]

x + 3 = 4

What would you do?

[golden bramble]

alieen i think this guy has to relearn the basics of maths

this wont do

[ember sorrel]

yeah

[golden bramble]

lets teach him the fundamentals of maths

[silent burrow]

He can learn it now!

[golden bramble]

😎

letsgo

[ember sorrel]

oh

[silent burrow]

Lezz go

[ember sorrel]

eh

[silent burrow]

x + 3 = 4

Tell me the value of x

[ember sorrel]

uhmm

[silent burrow]

□ + 3 = 4

[golden bramble]

subtract 3 from both sides, we got:
x + 3 - 3 = 4 -3
<=> x = 1

[silent burrow]

What is □

[ember sorrel]

1?

[golden bramble]

YESS

[silent burrow]

Yes, and cuh wrote it in the algebra way

[golden bramble]

HE DID IT

[ember sorrel]

oh well

[golden bramble]

im so proud of him lil alien 😭

[silent burrow]

What you basically did in your head was that you said 4 - 3 = 1 so we should have 1 to add up to 4

[golden bramble]

anyway yall i gtg do my assignments

bye

[silent burrow]

Bye

[ember sorrel]

byee thank you

[silent burrow]

Alright

[golden bramble]

😀

[silent burrow]

when you have
x + 3 =4

[ember sorrel]

yeah

[silent burrow]

Just subtract both sides with 3

what do you have rn?

[ember sorrel]

Can it be divide?

[ember sorrel]

A pen

[silent burrow]

[silent burrow]

Well, no

[ember sorrel]

Why

[silent burrow]

When you divide everything is divided

[ember sorrel]

ho would i know if it's divide times or sub

[silent burrow]

Depending on the situation

[ember sorrel]

oh

[silent burrow]

The only thing you have to know

Is that just isolate x

Alright

[ember sorrel]

What's isolate?

[silent burrow]

That's the only thing to do

Let me show you examples

[ember sorrel]

Mkay

[silent burrow]

Look

[ember sorrel]

Yeah

[silent burrow]

In order to get rid of 1

I simply subtract one

[ember sorrel]

Oh ok

[silent burrow]

Now look at this one

We have 2x

[ember sorrel]

Yeah

[silent burrow]

We have isolated 2x but now x

Now we will do the exact same thing you told a minute ago, " dividing"

[ember sorrel]

Okok

[silent burrow]

Does that make any sense?

[ember sorrel]

not really

[silent burrow]

Imagine 2 × □

[ember sorrel]

ye

[silent burrow]

And I want the amount of □

But the thing says we have 2 □

So I want half of the 2□

In order to have □ it self

Because :

2 □ = □ + □

And

□ = □

Btw can I ask you what grade are you?

[ember sorrel]

10 :›

[silent burrow]

Good

[ember sorrel]

why

[silent burrow]

Why not?

[ember sorrel]

i dunno

[silent burrow]

You can learn these things easily trust me 😎

[ember sorrel]

yes sir

[silent burrow]

Let me think about the correct way of explaining it, gimme a second

[ember sorrel]

okayy

[silent burrow]

I want you to tell me the answer

Don't multiply them

Try to simplify it

[ember sorrel]

What

wym by that

[silent burrow]

Alright have you ever heard about that you can remove numbers that look exactly the same in division?

[ember sorrel]

yeah

[silent burrow]

Alright which ones look exactly the same

[ember sorrel]

So like remove 3?

[silent burrow]

Yep

[ember sorrel]

And then divide 10 and 5?

[silent burrow]

Yes!!

[ember sorrel]

ohhh

so 2

[silent burrow]

And you know what's funny

[ember sorrel]

What

[silent burrow]

10 can be written as 5 × 2

We have 5 on both parts

[ember sorrel]

Yeah

[silent burrow]

Then you remove 5s and you end up with 2

Let me send you an example

One more I mean

[ember sorrel]

Okok

[silent burrow]

Simplify this question and gimme the answer

[ember sorrel]

Dang

[silent burrow]

It doesn't matter how big the numbers are

Just remove things that look the same

[ember sorrel]

oh then 10

[silent burrow]

Yes!!!

Exactly

[ember sorrel]

Yuhh

[silent burrow]

See, I told you, you will learn it fast

[ember sorrel]

oh yeah thank you thank you

[silent burrow]

Now do this one

[ember sorrel]

mkay

[silent burrow]

Hint: 6 = 2×3

[golden bramble]

you got some patience buddy

also hello

im back

[silent burrow]

Hi

[ember sorrel]

Oh 1

[silent burrow]

Yes exactly

That's correct

[golden bramble]

damn alien what did you do to him

hes learning too fast

thats great to hear actually

[silent burrow]

Lol I didn't do anything, he learns fast

Alright now let's go on with the useful ways of using division

[ember sorrel]

Okay

[golden bramble]

bet

[silent burrow]

We are getting closer to the parts where we are using this technique to answer actual questions

[ember sorrel]

2x?

[silent burrow]

Yep!

Alright now I will tell you something REALLY REALLY IMPORTANT

[ember sorrel]

yes sirr

[silent burrow]

What do you think about this? Can we remove 2s?

The short answer is NO

Absolutely not

[ember sorrel]

oh my

Why

[silent burrow]

Never make this mistake alright

[ember sorrel]

Yes yes

[silent burrow]

Let's do it and see if it's okay to remove them

If we delete 2

[ember sorrel]

Okok

[silent burrow]

We end up with 1 right?

[ember sorrel]

Ye

[silent burrow]

Now let's do it direc

Directly

[ember sorrel]

eh

[silent burrow]

2+1/3

No sorry

2+1/2

3/3

[ember sorrel]

mkay

[silent burrow]

Bruh

3/2

They are not equal do you agree?

[ember sorrel]

Ye

[ember sorrel]

1?

[silent burrow]

Yes

Why do you say ?

When you do something directly, everything is gonna be right

[ember sorrel]

oh

then what

[silent burrow]

Do this one as well

[ember sorrel]

oh i don't know this one

can it be 7 over 5?

no?

[silent burrow]

Yes why not

[ember sorrel]

Oh

[silent burrow]

7/5

That's completely correct

[ember sorrel]

oh well

[silent burrow]

I gotta go rn

Cya

[ember sorrel]

oh my

oki bye bye thank you very much

[silent burrow]

I’m back

First of all, hi

I highly suggest you watch some algebra videos to learn how they work cuz you WILL need them in high school

[silent burrow]

And after doing that, start solving the questions you had sent

I will try my best to help you (and any other person here in the math server), just ask whenever you get stuck 😉