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25

Part of 2016 AMC 8

Problems(1)

Semicircle Inscribed in an Isosceles Triangle

Source: 2016 AMC 8 #25

11/23/2016
A semicircle is inscribed in an isosceles triangle with base 1616 and height 1515 so that the diameter of the semicircle is contained in the base of the triangle as shown. What is the radius of the semicircle?
[asy] unitsize(0.25cm); pair A, B, C, O; A = (-8, 0); B = (8, 0); C = (0, 15); O = (0, 0);
draw(arc(O, 120/17, 0, 180)); draw(A--B--C--cycle); [/asy]
<spanclass=′latex−bold′>(A)</span>43<spanclass=′latex−bold′>(B)</span>12017<spanclass=′latex−bold′>(C)</span>10<spanclass=′latex−bold′>(D)</span>1722<spanclass=′latex−bold′>(E)</span>1732<span class='latex-bold'>(A) </span>4 \sqrt{3}\qquad<span class='latex-bold'>(B) </span> \dfrac{120}{17}\qquad<span class='latex-bold'>(C) </span>10\qquad<span class='latex-bold'>(D) </span>\dfrac{17\sqrt{2}}{2}\qquad <span class='latex-bold'>(E) </span>\dfrac{17\sqrt{3}}{2}
AMC 82016 AMC 8