Name: Pythagorean theorem and radii of circles | Circles | Geometry | Khan Academy
Uploaded: 2016-02-21T09:16:30.000Z
Duration: 5 min 53 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

Adverbs of degree

is O. Find the exact length of OA, CD, and OF.

It's one of the two shorter sides of a right triangle.

so we're not going to be able to figure out CD

OF is one of the two shorter sides of a right triangle.

OA is the hypotenuse of a right triangle,

and they've given us the two other sides.

So we know that 7 squared, let's call this x.

is going to be equal to the length of OA squared.

let's do a multiplication right over here

And so let's think about what this is going to be.

And this is going to be the same thing as 50 plus 575.

I just took one away from this and added one here.

And you might recognize that 25 times 25 is 625.

And if you don't believe me you could multiply that out

Or another way of thinking about it, the exact length of OA

Now, how can we somehow use that information

all of their hypotenuses are a radius of the circle,

Well, we just figured out the radius of the circle is 25.

So OG is going to be 25, and OC is going to be 25 as well.

So now we just have to apply the Pythagorean theorem a few more

let's just call that, I don't know for the sake of argument,

that a squared plus the square root of 141

squared-- I'll just write that as 141-- so plus 141 is going

to be equal to 25 squared, which we already know to be 625.

So let's do 625 minus 141 we get 5 minus 1 is 4.

And then 12 here, and we can put a 5 there.

Actually, I'll just try to do a prime factorization here

So 484 is 2 times 242, which is 2 times 121, which

So another way of thinking about it is this

is 2 squared-- so 484, I'll write it over here.

484 is equal to 2 squared times 11 squared.

So in this case a is equal to-- let me just clean all that up

so I have some space to work with-- a is equal to 22.

a is equal to 22, so that's equal to 22 right here.

Let's just call this, I don't know, I've already used a.

So we see that b squared plus 15 squared, which

is the same thing as 225-- 15 squared is 225--

Subtract 225 from both sides you get b squared is equal to 400,

and the square root of 400 is pretty easy to calculate.

So segment OA is 25, CD is 20, and OF is 22.