For this question, you can do Pythagorean Theorem to solve WY. Since WY is tangent to the circle, we know that the triangle is a right triangle.
We know one leg is 9 and the other leg, WY is unknown. But, we do know the hypotenuse.
XY is 6 but PX is unknown. If you think about it, PX is a radius of the circle and we know that the radius is 9 since PW is also a radius of the circle. So, the hypotenuse is 6 + 9 = 15.
We know one leg is 9 and the hypotenuse is 15. We need to find the other leg and we can.
Pythagorean Theorem states that
a^2 + b^2 = c^2 where a and b are the sides of the triangle and where c is the hypotenuse. Using basic algebra, we can alter the equation to find a leg using the hypotenuse and one other leg.
c^2 - b^2 = a^2
All I did was solve for one leg and it doesn't matter what leg you solve for. Let's plug in the numbers.
15^2 - 9^2 = a^2
225 - 81 = a^2
144 = a^2
Take the square root on both sides to get "a" by itself with raising it to the second power.
12 = a
So, the last leg is 12. Hope this helped and good luck!
