Question

Help?(:
{Find x & y.}

Answer 1

i worked it out partly.. and got this as my answer.(: Hope it helps.

Answer 2

k

Answer 3

That gives
5y = 12x

Answer 4

The product of the lengths of the segments of one chord equals the product of the lengths of the segements of the other chord.

Answer 5

In english please? ..you lost me there.

Answer 6

Now look at right triangle TRV, with right angle R.

Answer 7

ok

Answer 8

This is a chord.

Answer 9

Now you have a circle with two intersecting chords.

Answer 10

k

Answer 11

One chord has two segments of lengths a and b.
The other chord has segments of lengths c and d.

Answer 12

ok?

Answer 13

.sure?

Answer 14

can we plug in the numbers from the problem? cuz im still not getting it..

Answer 15

I'm trying to first explain the reason why you can write the equations.
You have two variables, x and y. You need two equations.
We're going to use the chords to get one equation.
We're going to use the right triangle to get the second equation.

Answer 16

k

Answer 17

In your problem, one chord has segments of lengths 5 and y.
The other chord has segements of lengths 12 and x.
That means 12x = 5y
This is our first equation.

Answer 18

Now for the second euquation, we use the right triangle TRV with right angle R.

Answer 19

One leg measures 15.
One leg measures y.
The hypotenuse measures x + 9.

Answer 20

Now we use the Pythagorean Theorem using the lengths of the sides to get our second equation.
15^2 + y^2 = (x + 9)^2

Answer 21

Now we have our two equations. We need to solve them simultaneously for x and y.

Answer 22

that is necessarily not the hypotenuse

Answer 23

does not say SR is passing through the center

Answer 24

???

Answer 25

@dan815 You are correct.

Answer 26

:)

Answer 27

So was my answer wrong, or not?

Answer 28

I was thinking SR is a diameter, but it does not state it is anywhere.

Answer 29

yeah i thought so at first too, it would have this a lot simpler

Answer 30

Soo.....?

Answer 31

That means we need a different method of getting the second equation.
The first equation is still good, 12x = 5y.
Now let's work on the second equation using the segments of the tangent and secant TQ.

Answer 32

The secant is made up of two segments. The external part (outside the circle) and the internal part (inside the circle).

Answer 33

The relaitionship between the lengths of the segments is:
(whole secant) * (external segment of the secant) = (tangent)^2

Answer 34

In our problem, the entire secant is 9 + x + 12 = x + 21
The external part of the secant is 9
The tangent is 12

Answer 35

doesnt it make you stare at it

Answer 36

theres some crazy symmetry going on in that picture

Answer 37

Ok im really confused now.. Can i just get a simple yes or no to my question? Was it wrong or not? Ive spent over 20 minutes on this i have to move on to other problems. Thanks for trying guys.