Question

MEDAL AND FANNED REWARDED
Solve for x

http://prntscr.com/36trr1

Answer 1

You're given that OP = 15, FG = 40 and FG is orthogonal to OP, so you have a right triangle with sides of length 15 and 20. So first find OF, by the Pythagorean theorem:

\[OP^{2} + FP^{2} = OF^{2}\]\[15^{2} + 20^{2} = 225 + 400 = 625 = OF^{2}\]\[\sqrt{625} = 25\]
So the radius of your circle is 25, which is pretty much all you need to know to solve the rest of it. You can now use a similar process to find the length of RQ and solve the right triangle given by OQR:
\[625 = x^{2} + (\frac{RS}{2})^{2}\]\[625 = x^{2} + 15.5^2\]\[\sqrt{625-15.5^{2}} = 19.6150 \approx 19.6\]

So the answer is d.

Answer 2

thank ou

Answer 3

where did the 400 come from

Answer 4

@bhl6180

Answer 5

You're given that FG = 40, and half of FG is one of the sides of your triangle. So you take 1/2 * 40 = 20^2 = 400 in your Pythagorean equation.