View source for 2016 AMC 8 Problems/Problem 25

25. A semicircle is inscribed in an isosceles triangle with base <math>16</math> and height <math>15</math> so that the diameter of the semicircle is contained in the base of the triangle as shown. What is the radius of the semicircle?

[Diagram]

<math>\textbf{(A) }4 \sqrt{3}\qquad\textbf{(B) } \Dfrac{120}{17}\qquad\textbf{(C) }10\qquad\textbf{(D) }\Dfrac{17\sqrt{2}}{2}\qquad \textbf{(E) \frac{17\sqrt{3}}{2}</math>

==Solution==
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