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2016 AMC 8 Question 25

AMC8 · 2016 AMC 8

Question 25

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

Question illustration
  1. $ 4 \sqrt{3} $
  2. $ \dfrac{120}{17} $
  3. $ 10 $
  4. $ \dfrac{17\sqrt{2}}{2} $
  5. $ \dfrac{17\sqrt{3}}{2} $