please help me thank you

[near lily]

Find the measurements of the following segments.

[boreal gale]

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[wise gust]

what did they teach in class?

[near lily]

I have no idea I'm sorry

i couldn't focus during class

but they said solve it with your own formula?

[wise gust]

you must have some class material

there's a lot of way to do something

[next fox]

@glacial bolt try it

[glacial bolt]

I don't know how to help him

[near lily]

awoop

[glacial bolt]

I only know the direct answer

Cant really guide him

[near lily]

are direct answers allowed? no?

[glacial bolt]

Nope

[near lily]

uh oh

[next fox]

Do you know how to solve tho ? Or just answer

[glacial bolt]

I think we need to draw altitude

In 3

[near lily]

oh

what's that

[modern girder]

use these 2 theorems

[near lily]

oh thank you I will try

[near lily]

i can't do it I'm sorry i don't know how

[next fox]

Ok let's see the 1st one

Let's take intersection point as P

[next fox]

And focus on first theorem from this

[next fox]

We can take distance 5 as A, distance 5+8 as B, distance 6 as C and 6+x as D ?

I wanted to write points but not on pc atm

[next fox]

Well anyways, from this we know PA, PB, PC and we gotta find PD

@near lily can you do it now 👀

[near lily]

i'm trying to get it

but i can't I'm so sorry

[next fox]

It's ok it's ok

[near lily]

i don't understand at all

[next fox]

So the theorem says

PA x PB should equal PC x PD right ?

[near lily]

Yes sir

[next fox]

Now PA is 5

PB is 13

[near lily]

How is that

Oh nvm

[next fox]

PA was 5

And AB is 8

[near lily]

Oh yes yes

[next fox]

Okie, now PC is 6

And PD is 6+x

So

6(6+x) = 5(13)

[near lily]

yes

[next fox]

6+x = 65/6

x = 29/6

[near lily]

what happened to it

divide?

[next fox]

To what 👀

[next fox]

Oo it's still there

29/6

[near lily]

But where did you get 29?

[next fox]

Ohh

I took +6 on other side

It was 6+x = 65/6

x = (65/6) -6

x = (65-36)/6

[near lily]

Ohhh

okok

[next fox]

Okie now next question

[near lily]

Wait what

[next fox]

Also don't you think next theorem is just the same

[near lily]

No sir

it confuse me

[next fox]

Oooo

Wait lemme get on pc, first let's understand next theorem

[near lily]

So the answer is 6?

[next fox]

Nah

[near lily]

Oh

[next fox]

It's 29/6

[near lily]

oh my

[next fox]

Which would be almost 5

[near lily]

wait they said the answer was in fraction

[next fox]

Unless my calculation went wrong somewhere

[next fox]

Oo then calculations are probably right

I don't like such answers either

Why 29, give us 30

It would become a perfect 5

[near lily]

so then it's 5?

[next fox]

Nah

29/6

[near lily]

oh my

now what we do sir

[next fox]

okie now I m on pc

lets look at next theorem

then next question

[near lily]

Okioki

Yuhhhhh

[next fox]

soo in first theorem, we had 2 points on each side, A,B and C,D

in this theorem we have a side with only 1 point

but looking at first theorem

we multiplied the distance when we first touched circle, and distance when we touched it 2nd time

so with only 1 point, we touch only once

[near lily]

why would we touch that

[next fox]

no no not us

the line

[near lily]

We can't touch the line?

[next fox]

I mean the point where line makes contact with circle

A,B,C,D,T

[near lily]

there's a T?

[next fox]

yee in 2nd Theorem

check the 2nd theorem once

its totally different yet totally same

[near lily]

Oh sori sori

i thought we only talking about the first

now what happened

[next fox]

Oo you understood how 1st works right ?

[next fox]

we are finding 2nd theorem

in first we had 2 points on both sides so we did PA x PB = PC x PD

but this time we only have 1 point in bottom side

[near lily]

yes sir

[next fox]

in this case

what we do is PA x PB = PT x PT

multiply it with itself, it touched, and then it untouched

[near lily]

oh

[next fox]

T is playing role of both C and D

now lets try this

[near lily]

Yesyes

[next fox]

look at 5th one

[near lily]

Yes sir

[next fox]

first we find y 👀

[near lily]

y

[next fox]

yes

[near lily]

why not x?

[next fox]

so how many times does that line touch the circle

[next fox]

because that uses the same theorem as last question

[near lily]

one time?

[next fox]

yup

what do you do when it touches only once 👀

[near lily]

i dunno ¯⁠\⁠(⁠°⁠_⁠o⁠)⁠/⁠¯

[next fox]

we multiply it with itself

[near lily]

oh okay okay 👍

[next fox]

so whats PA

and PB

in this question

[near lily]

hmmm

4?

[next fox]

yup

and one more

[near lily]

Yasss

hmm

14?

[next fox]

nope

[near lily]

Oh

How so

[next fox]

you have to take distance from P

the point where lines intersect

[near lily]

so 6?

[next fox]

nope

https://media.discordapp.net/attachments/1194650910010396775/1194673697789853807/Untitled17_202401100022053.png?ex=65b13595&is=659ec095&hm=30d1bbb645429f37a38c2e34a8e09c5728e33f160d5c836878b7f1bf11aa5303&=&format=webp&quality=lossless&width=731&height=560

[near lily]

Waaaa

Y?

[next fox]

from the point where they intersect

to the end

[next fox]

nope

[near lily]

X?

[next fox]

nope

[near lily]

oh my goodness

[next fox]

you tried each value written there lol

[near lily]

but why tho

Is it the dot thingy?

[next fox]

1st, A,B are on same line right ?

[next fox]

nope

[near lily]

oh

[near lily]

Yes sirr

[next fox]

so, on one line there is 4 and 14

so 14 was a close guess

but 14 is distance from A to B right ?

[near lily]

Yeah

kinda

[next fox]

A being point where it first touched circle

[next fox]

but we don;t want A to B

we want P to B

so we can add distances from P to A then A to B

[near lily]

mkkayy

[next fox]

so what was distance from P to A

[near lily]

do i have to multiply something?

[next fox]

nope

wait lemme mark everything

[near lily]

Yes please

[next fox]

now whats PA in this @near lily

[near lily]

4!

[next fox]

yup

whats AB

[near lily]

Yassss

and then

[next fox]

👀

[next fox]

we have to find PB

so PB should be PA + AB right ?

[near lily]

yeahhh

[next fox]

so whats AB

[near lily]

14?

[next fox]

yup

so whats PB

[near lily]

i'm sorry i have no idea

Waitt

[next fox]

👀

[near lily]

4x14?

[next fox]

why multiply

[near lily]

Oh

4+14?

[next fox]

yes

[near lily]

why not

[near lily]

YAUUHH

[next fox]

PB = PA + AB right ?

[near lily]

oh ye

[next fox]

now we know PA and PB

[near lily]

Yes we do

[next fox]

PA x PB is gonna equal PE x PE

right

[near lily]

Yesyes

[next fox]

whats PE

[near lily]

Uh

Y?

[next fox]

yup

[near lily]

Yes

[next fox]

so y^2 = 4 x 18

[near lily]

I thought it was plus?

[next fox]

18

my bad

[next fox]

PB = PA + AB

but PE^2 = PA x PB

[near lily]

hmmm mkay mkay

[next fox]

so y = $\sqrt{72}$ ?

[upper flax]

Akki#gtfoanemia#ViataGod

[near lily]

Oh wait wait

but where did you get 18 tho?

you plus it before?

[next fox]

you told me

[next fox]

here

[near lily]

Oh yeah

but why it turned 72

how tho

[next fox]

Ooo

$y^2 = 4 \cross 18$ right

[near lily]

Yeah

[upper flax]

Akki#gtfoanemia#ViataGod

[next fox]

there

[near lily]

okioki

[next fox]

4 x 18 = 72

[near lily]

Yes yes

[next fox]

so $y^2 = 72$

[upper flax]

Akki#gtfoanemia#ViataGod

[next fox]

bruh whats going on with me lol

typos everywhere

anyways

$y=\sqrt{72}$

[upper flax]

Akki#gtfoanemia#ViataGod

[near lily]

What happened to the 2?

[next fox]

that was square

[near lily]

Yeah

[next fox]

so it became square root

[near lily]

Ohhh

Okay okay

what we do now tho

[next fox]

now we have y

its $\sqrt{72}$

[upper flax]

Akki#gtfoanemia#ViataGod

[near lily]

Ohhh my

but then there's still x?

wat we do with it

[next fox]

yee

now we find x

whats PC

[near lily]

6?

[next fox]

how

[near lily]

cause I see it

[next fox]

look from P to C

[near lily]

Yeah

I see x

[next fox]

C is the point from where arrow is fron

[next fox]

now PD

whats PD

[near lily]

6?

[next fox]

nope, thats CD

[near lily]

oh

[next fox]

what would PD be 👀

[near lily]

is it x + 6?

[next fox]

[near lily]

I'm right?

[next fox]

yes

[near lily]

yassss 🥳

[next fox]

now, PC x PD = PA x PB right

[near lily]

yessir

[next fox]

what was PA x PB

ohh x is gonna get messy

[near lily]

oh no

[near lily]

4+14?

[next fox]

that was PA x PB ?

[near lily]

was it?

[next fox]

this is just PB

[near lily]

oh

then 4 x 18?

[next fox]

yes

[near lily]

Yuuhhh

now what we do

[next fox]

whats 4 x 18 ?

[near lily]

72?

[next fox]

yup

so x(x+6) = 72

$x^2 + 6x -72 = 0$

[upper flax]

Akki#gtfoanemia#ViataGod

[next fox]

now what if I write

6x as 12x - 6x

[near lily]

eh

[next fox]

$x^2 + -6x + 12x -72 = 0$

[upper flax]

Akki#gtfoanemia#ViataGod

[next fox]

this is right, right ?

[near lily]

i don't know..

[next fox]

whats 12 - 6

[near lily]

6?

[next fox]

whats 12x - 6x

[near lily]

6x?

[next fox]

yes

[near lily]

oh oki

[next fox]

so I wrote 6x as 12x - 6x

[next fox]

now lets write it like this $x(x-6) + 12(x-6)$

[upper flax]

Akki#gtfoanemia#ViataGod

[next fox]

$(x+12)(x-6) = 0$

[upper flax]

Akki#gtfoanemia#ViataGod

[near lily]

kkk

[next fox]

what are the 2 values when this will be 6 👀

[near lily]

x?

[next fox]

yee

2 values of x

when it will all become 0

[near lily]

yes

[next fox]

either x+12 should be 0 or x-6 should be 0 right

[near lily]

yes sirrr

[next fox]

at what x does x+12 = 0

[near lily]

I don't know

6?

[next fox]

if x = 6 then x+12 = 0 ?

[near lily]

yeah?

[next fox]

if x=6, x+12 = 18

we want it to be 0

[near lily]

hm

how can it be 0?

[next fox]

what if x = -12

wouldn't it be 0 then ?

[near lily]

Will it tho?

[next fox]

-12+12 = 0

[near lily]

oh

[next fox]

thats 1 solution, but it can't work

as we can't have negative distance

so there has to be another solution

[next fox]

which we get from here

either (x+12) is 0 or (x-6) right

lets see when x-6=0

so at what x is x-6 , 0

[near lily]

uh

i don't know i'm sorry

[next fox]

x-6=0

find x

[near lily]

how do I do that tho

[next fox]

take 6 to other side

x-6 = 0

then x = +6

[near lily]

then what

[next fox]

x = 6

thats the answer

[near lily]

oh

then what we do with it

[next fox]

nothing

[near lily]

wait what

that was the x in the circle thingy?

i'm guessing it is

oh my then thank you very much you're very helpful sir

thank you thank you 💞

[next fox]

its this x

ooo you mean angle

it wasn't angle