Circles or whatever u call it , come help me out lol

[spiral sigil]

yes

[waxen hornet]

1. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
2. Wait patiently for a helper to come along.
3. Once someone helps you, say thank you and close the thread with:

   +close
   

4. Feel free to nominate the person for helper of the week in #helper-nominations
5. Do not ping the mods, unless someone is breaking the rules.
6. If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[vague spire]

What do you need help with, exactly?

[spiral sigil]

all of these

i assume theres the same idea or "formula" in all of them

i need overall explanation

[vague spire]

What have you tried?

[spiral sigil]

this is the first part and the other ones the last

nothing because i dont know what to even try

https://tenor.com/view/terraria-gif-25158873

[vague spire]

Well, for the first several exercises you can use the two secants theorem.

Note that this also works for tangents, as they can be seen as a degenerate case of a secant when two points coincide.

[spiral sigil]

hmm

ill try

i most likely wont be able to do it brb

ok so how am i supposed to use that formula here

Very good drawing btw

[vague spire]

You didn't draw it correctly. The top line in (1) is a tangent.

[vague spire]

Right. So, now try applying the theorem.

[spiral sigil]

How lol

sorry im a complete meathead

[vague spire]

Compare your picture to this picture.
Note that in your case one of the lines is a tangent. So, for example, if in this picture the top line was a secant, the the points B and B' would coincide, in which case we would have AB^2 = AC*AC'.

[spiral sigil]

its different

both lines are inside on that formula

here other ones a tangent

[vague spire]

Well, yeah, and I just said what happens when we have a tangent...

[spiral sigil]

I dont know what coinciding means..

i study math in georgian language and not englishj

[vague spire]

To coincide means to occupy the same space.

Well, I also don't study math in English.

[spiral sigil]

I dont have any connection with english math

except when i come here for help

[vague spire]

Oh. I see.

[spiral sigil]

can you solve it

ill understand

[vague spire]

You need to be able to solve it yourself.
As I said above, in case of a tangent we get this. Point B and B' coincide, so we get AB' = AB, thus getting this formula.

[spiral sigil]

🧠

🔥

is it

4

ac' = 16

ab2 = 4

[vague spire]

Wait, no.

In our case for the secant the short segment is 4, while the long segment is 12 + 4 = 16.

So, what equation do we get for x?

[spiral sigil]

16x4?

is it 8

its 8

innit

i got it

has to be 8

[vague spire]

Yes, x = 8.

[spiral sigil]

16x4 = 64 and root is 8

next ones fucked up

what is 4 <2

[vague spire]

What do you mean?

[spiral sigil]

is it 16

[wanton iron]

just treat it as a number

[spiral sigil]

oh

ok

[wanton iron]

it's not

[spiral sigil]

8 ?

32?

[wanton iron]

no

[spiral sigil]

its either 8 or 32

[vague spire]

No. 4√(2) is 4√(2), why would it be 16?

[wanton iron]

yeah

[spiral sigil]

what is it

[vague spire]

Wait, you don't know what a square root is?

[spiral sigil]

I do

i forgot

💀

[vague spire]

Huh...

[wanton iron]

oh-

[vague spire]

You really need to review some algebra first, then.

[wanton iron]

this might take a while

[spiral sigil]

so what is

4 square 2

is it not 32

[vague spire]

Not sure what you mean. 4√(2) is 4√(2), that's it.

[wanton iron]

square root, not square

[spiral sigil]

Oh ok

Im fucked

[wanton iron]

look, the square root of 2 is irrational

[spiral sigil]

my lifes ruined

[wanton iron]

basically it can't be a normal number

[wanton iron]

no it's not

[vague spire]

You need to review some topics in algebra and geometry, then. I don't think you can solve these exercises otherwise.

[spiral sigil]

What do ido

[wanton iron]

so 4√(2) can't be simplified further

[wanton iron]

practice

[spiral sigil]

Ok

how do i find X

[wanton iron]

yeah

[wanton iron]

which question

[spiral sigil]

thats why i couldnt find it

[wanton iron]

so that's the length of the tangent

[vague spire]

Well, the approach is the same as in (1).

[spiral sigil]

But theres nothing to multply on

[wanton iron]

yeah I need to see the question

[spiral sigil]

i only have 1 number

[spiral sigil]

find X

thats all

[vague spire]

It's (2) in the picture above.

[spiral sigil]

how do i use the formula

when theres only 1 number

what do i multiply on

[vague spire]

Note that you are also given that the two pieces of the secant are equal.

So, you can find the short and long segments in terms of x.

[spiral sigil]

😭

Im cooked

[wanton iron]

ok idk how to solve this-

[spiral sigil]

im gonna fail the exams and become a soldier

and get killed in battle

[vague spire]

Well, we use the same formula as in (1).

[spiral sigil]

this makes me feel better

[vague spire]

Don't talk nonsense. You just need practice.

[wanton iron]

idk the formula-

[spiral sigil]

i have 3 months left

@vague spire

want to review a sample exam?

[vague spire]

I've also written it above.

[spiral sigil]

see if u think i can learn them in 3 months

[wanton iron]

alr

[vague spire]

Plenty of time.

[spiral sigil]

https://naec.ge/uploads/postData/20-23/ერთიანი ეროვნული გამოცდები - ტესტები/მათემატიკა/Version_1.pdf

thats the last years exam

of math

check it out

i need 20 points

[vague spire]

What do you mean by "learn"? Surely you've learned it all, just forgot most of it.

[spiral sigil]

yeah i did

lol

not in school

i learnt them this year

binge learning is hard to memorize

i never studied math in school

[wanton iron]

oh-

[vague spire]

Devote a couple of weeks to reviewing geometry and algebra.

[spiral sigil]

https://naec.ge/uploads/postData/20-23/ერთიანი ეროვნული გამოცდები - ტესტები/მათემატიკა/Version_1.pdf

[vague spire]

Read the theory, practice some problems.

[spiral sigil]

check this exam out

weird link but its official country link

this is the fourth question

its basic triangle geometry

ive been through triangles

yet i still cant solve it

¯_(ツ)_/¯

[vague spire]

I can't accurately evaluate it for two reasons:

1. Can't read most of it.
2. The exercises I can read are easy to me, as those are still high school level questions.

[spiral sigil]

( find BAC)

[vague spire]

That's why you need to re-read the theory and solve some practice problems.

[spiral sigil]

Woudl u believe me if i told you 80 percent of us fail

and 20 points from 51 can get you into any university you want

in the whole country

💀

[vague spire]

That just means that it is a bad school.

[spiral sigil]

its national exams

[wanton iron]

yeah true

[spiral sigil]

its not signle school

also yes my schools bad ,we smoke vapes and cigarettes in class infront of the teachers

[vague spire]

Like, seriously. 80% of people failing is most definitely the fault of the teachers.

[spiral sigil]

and they cant do anything about it

[spiral sigil]

its approximate

not exactly

but half of us surely do fail

[vague spire]

Doesn't matter. If less than 70% of people pass a class, that's pretty catastrophic.

[wanton iron]

actually

[spiral sigil]

its not class

its national exams

its like SAT

to get into university

its after school

im in 12th grade,

[vague spire]

Again, doesn't matter.

[spiral sigil]

most of nowadays our boys want to be gangsters

[wanton iron]

it's an exam, you can pass it

[spiral sigil]

they are tryna be street boys and thiefs

[vague spire]

Huh...

But why?

[wanton iron]

i don't think it's like JEE advanced

[spiral sigil]

we call them "thief in law "

its a gang

[spiral sigil]

bad influence

[vague spire]

From who?

[spiral sigil]

https://en.wikipedia.org/wiki/Thief_in_law

[spiral sigil]

other street boys

[spiral sigil]

they are tryna be this

or just hood boys

its hard to explain in english

[vague spire]

Well, I know what that is, but this hasn't been like it in my case since, like, the 1990-s.

[spiral sigil]

its the most popular in my country

we are pretty much "saving" that thing

[vague spire]

Maybe early 2000-s, but that's a stretch.

[spiral sigil]

we have the most vor v zakones

[vague spire]

Hm... That's sad.

[spiral sigil]

modern versions are the worst

believe it or not, there was respect from vor v zakones

they never touched innocent, or elderly

or anything like that

nowadays they just tryna scare people and act tough ( talking about the young ones)

fake wannabes who are pieces of shit , with 0 respect or any knowledge about it

Whatsoever

all they want is you to look in their eyes once for them to start a fight

[wanton iron]

ok um-

[spiral sigil]

yes math

indeed

lets go back

[wanton iron]

it sounds like a shitshow there

[spiral sigil]

its not too hard to avoid them

lmao

I have connections too

so im safe

[wanton iron]

all the more reason why you have to pass your upcoming exam

[spiral sigil]

Indeed

[wanton iron]

ok you solved Q1 right?

[vague spire]

Still, you really do need to review the material first.

[spiral sigil]

i undersatnd q1

[wanton iron]

how did you solve it?

[vague spire]

Solving problems without knowing the proper theory will take far more time than needed.

[spiral sigil]

What exactly

[wanton iron]

ok true...

[spiral sigil]

I cant just overlook the whole geometry

you gotat be specific

[vague spire]

Geometry and algebra of the grade you're in.

[spiral sigil]

i know shit right now right? i been studying for 6 months

and i barely know shit

[wanton iron]

but honestly i think he just needs some logic to solve these

[spiral sigil]

i have a teacher

God rest his soul, i dont wanna blame him or anyhting

but due to his sickness, i lost 2 months of math

He passed away , he was a great teacher

now im with a different teacher and he started me all over again

so i gotta do an academical comeback

or im ruined

[wanton iron]

ok...

[vague spire]

Unfortunately, Luki said they don't remember the formulas, so logic alone won't help much.

[wanton iron]

oh-

[spiral sigil]

which formula

This thing im asking for help on is new

im supposed to learn it today

every time i come here its for extra knowledge

[wanton iron]

oh

[spiral sigil]

how do i explain this

basically im pre learning

[wanton iron]

the secant one

[vague spire]

Ohh...

[spiral sigil]

im going through this right now

[vague spire]

Well, you should've started with that 😅

[spiral sigil]

i have never seen this shit before in my life

lol

lord you thought i was re-learning

?

🤣

[wanton iron]

can someone pin this

[spiral sigil]

i understand this theoremm

yet i dont understand how to use it

[wanton iron]

actually

[spiral sigil]

when theres nothing to multiply on

[wanton iron]

there actually is

[spiral sigil]

theres only 4√2

and an X

[wanton iron]

see the circle divides the secant into 2 halves right?

[vague spire]

No Lifer, can you handle this? I think your explanation style is better suited here.

[spiral sigil]

yes?

[wanton iron]

both of which have a length of x

[spiral sigil]

thanks for the help anyways bro ❤️

[atomic blade]

@spiral sigil has given 1 rep to @vague spire

[wanton iron]

I can only stay till 6 unfortunately

I'll ping you then

[spiral sigil]

im going soon anyways

i got math in 2 hours

🤣

[vague spire]

And how much is it for you now?

[spiral sigil]

english in 1 hours

[wanton iron]

5:30

[vague spire]

Ah, ok.

[wanton iron]

oh ok

[spiral sigil]

30 minutes is long enough bro

[wanton iron]

alr Luki

[spiral sigil]

ok lets start the grind

[wanton iron]

the circle divides the secant in half right?

[vague spire]

Anyway, thanks!

[atomic blade]

@vague spire has given 1 rep to @wanton iron

[spiral sigil]

peace out terrarian

[wanton iron]

both halves have a length of X

[spiral sigil]

yes

since its equal

[wanton iron]

alr

https://cdn.discordapp.com/attachments/1225404644684070992/1225407739468058624/image.png?ex=662104e4&is=660e8fe4&hm=90b9cfbe9be9d024bcbffe61e957b2b4bd7518049a236b268ee79f538ad7a36a&

[spiral sigil]

yes

[wanton iron]

now in this picture

$AB = 4\sqrt{2}$

right?

[cursive aspen]

No Lifer #GTFOanemia

[spiral sigil]

yes

[wanton iron]

and $AC = CC' = x$

[cursive aspen]

No Lifer #GTFOanemia

[spiral sigil]

yes

[vague spire]

Ah, yeah, if you need better pictures for theorem, ping me, I can make them in KOMPAS.

[wanton iron]

now $AC + CC' = 2x$

$AC' = 2x$

[cursive aspen]

No Lifer #GTFOanemia

[spiral sigil]

Ok

[wanton iron]

right?

[spiral sigil]

indeed

[wanton iron]

now look at what the theorem states

$AB^2 = AC\times AC'$

[cursive aspen]

No Lifer #GTFOanemia

[spiral sigil]

ab2 = X * 2x ?

[wanton iron]

yes!

[spiral sigil]

How do you solve this tho

then what

[wanton iron]

ok substitute the values

$(4\sqrt{2})^2 = x \times 2x$

[cursive aspen]

No Lifer #GTFOanemia

[wanton iron]

$32 = 2x^2$

[cursive aspen]

No Lifer #GTFOanemia

[spiral sigil]

What

[wanton iron]

um you know what $(4\sqrt{2})^2$ is right?

[cursive aspen]

No Lifer #GTFOanemia

[spiral sigil]

yes

16x2

[wanton iron]

yes

and 16x2 = 32

[spiral sigil]

indeed

[wanton iron]

and on the other side

AC = x

AC' = 2x

[spiral sigil]

ok

let me try

Ok

ok so ab2 = 32 ?

32 = x * 2x ?

[wanton iron]

yes

[wanton iron]

yes

[spiral sigil]

3x = 32 ?

[wanton iron]

no not 3x

2x^2

$x \times 2x = 2x^2$

[cursive aspen]

No Lifer #GTFOanemia

[spiral sigil]

yes

i get it

[wanton iron]

you're adding not multiplying

[spiral sigil]

2x^2 = 32

?

[wanton iron]

yessss

correct!

[spiral sigil]

so what is X

[wanton iron]

solve 2x^2 = 32

[spiral sigil]

How

i forgor

[wanton iron]

ok wait a bit

[spiral sigil]

alr

[wanton iron]

$2x^2 = 32$

$x^2 = 16$

[cursive aspen]

No Lifer #GTFOanemia

[wanton iron]

alr?

[spiral sigil]

oh

thats easy

so X is 4

[wanton iron]

now can you get the next step?

[spiral sigil]

damnn

thats wild

[wanton iron]

good job bro

now do you need help with Q3?

[spiral sigil]

ye

[wanton iron]

ok so you get $(2\sqrt{3})^2 = 2 \times (2+2r)$

[cursive aspen]

No Lifer #GTFOanemia

[wanton iron]

from the theorem

[spiral sigil]

ye

[wanton iron]

you understand how right?

[spiral sigil]

yes

nt

(2√3)2 = 12

no?

[wanton iron]

yes!

[spiral sigil]

why did u break it down

like that

[wanton iron]

2 = AC
2 + 2r = AC'

[spiral sigil]

oh ok

ok so

12 = 2x ( 2 + 2r )

[wanton iron]

yes

[spiral sigil]

12 = 4x + 4RX

or what did i just say

💀

[wanton iron]

no no there's no x

r is the variable here

you'll get
12 = 4 + 4r

[spiral sigil]

4r = 8

r=2

[wanton iron]

yep

ok Q4

notice the tangent common to both the circles

oh you're offline lol

alr bye Luki!

[spiral sigil]

@wanton iron sorry my lights went offf

+close