I need help with calculating the area of ABCO

[onyx jetty]

R = 10 and I need to find area of ABCO. I assume I need to find AB or BC sine I will calculate it with formula AO*AB, but idk how to find them.

[stable osprey]

Do you know the coordinates of B

[onyx jetty]

x no but y is 10

AB and BC are tangentialities

[stable osprey]

Solve its x coordinate first

[onyx jetty]

how?

[stable osprey]

Gimme a second

Do you know how to set line BC? With assuming its gradient being m

[onyx jetty]

uhh probably no? I dont learn maths in english

If its vectors then i do know them

[stable osprey]

It describes how steep is a slope

@onyx jetty are you still there?

[onyx jetty]

Yes

It doesnt say in the problem but I assume its paralel to x axis

[stable osprey]

okay
Do you know the form
(y-a)=m(x-b)
Which helps you assume a function of a line when you get a slope and a certain point?

[onyx jetty]

No i dont know this one

[stable osprey]

oh…

What forms have you learnt so far?

only y=ax+b?

[onyx jetty]

Aint no way this problem is that hard

Yes y = kx + b

[stable osprey]

Nah, it’s easy

only y=ax+b
And ax+by=c ?

Then how do you solve this question 💀

[onyx jetty]

Idk man

I might give up

[stable osprey]

Is this an assignment?

[onyx jetty]

I mean hw

[stable osprey]

I see

[onyx jetty]

Wont be graded

Teacher said try this one

And I cant seem to figure it out

[stable osprey]

You need the form I provided to solve this question

or else you need something like matrix

To rotate y=10

But it would be far far FAR more complicated than this

[willow dune]

OA=10
OC=10
AB=BC
angle A =angle C = 90
so angle AOC + angle ABC =180
these are the provided details

you start by constructing OB and find the coordinates of B by equating AB and BC

[stable osprey]

@onyx jetty I’ve managed to find a solution that may help you out

Set y=mx+k
m is the gradient
Plug in (6,-8) and state k with m

[onyx jetty]

Im all ears

[willow dune]

you dont know the slope of the two lines tho

so y=mx +c is useless in this situation

[stable osprey]

Just find it out 💀

[stable osprey]

It is useful

[willow dune]

thats not the problem here we need to find the area

[stable osprey]

Then just find out the slope, it’s solvable

[willow dune]

ye maybe a good idea

[stable osprey]

However, I’m interested in your idea as well

[willow dune]

it is simple

lemme explain

[stable osprey]

Sure

[willow dune]

when you equate the distance of AB and BC (which are equal) by taking B asa an arbitary point of (x,y) we will get the point B
after that we construct a diagonal OB and split it into two triangles
we know that tangents are perpendicular to the radius, therefore we can use the triangle area formula(0.5XbaseXheight), then sum up the two areas to get the total area of ABCO

[stable osprey]

But how do you find B in that way?

You don’t have the access to the other side

oh Ik your idea

Good one

[willow dune]

AB=AC because tangents from an external point are equal in magnitude

[willow dune]

THANKSSSS

[cloud bison]

The area is 195

[willow dune]

nobody here wants the answer

[stable osprey]

Well, mine is set line BC y=mx+k ( I initially want to set (y-a)=m(x-b) but he seems unfamiliar with the latter form)
Plug in (6,-8) and state k with m
After that, you’ll get mx-y=6m+8
use the line-point formula to state the distance between line BC and (0,0), as we know from the graph, the distance will be 10
Therefore, you’ll get a formula with m

[stable osprey]

True LOL

[willow dune]

we know the answer before your generation came into existence @cloud bison

[willow dune]

appreciatable.

but math is all about the shortest method so

I WIN

[stable osprey]

Yours too

[cloud bison]

got it by the same approach

[stable osprey]

But in terms of comprehensive, me win 😄

[willow dune]

ur method has a lot of brain and coordinate geometry base to solve

[stable osprey]

Speak of the solution

[cloud bison]

yeah

[stable osprey]

Where is the OP

[willow dune]

mine is Layman's

[stable osprey]

…

[willow dune]

vvanished into thin air

[stable osprey]

Bruh, imma go and solve other questions

Imma leave him

Cya fams

[willow dune]

Cya

[grave barn]

oh my method
find ac
then find the angle aoc using law of cosine
that angle aoc + angle B = 180
and angle andle abc = 1/2 angle B
angle obc = 1/2 angle B