MathDB

22

Part of 2017 AMC 8

Problems(1)

Semicircle in Triangle

Source: AMC 8 2017 #22

11/22/2017
In the right triangle ABCABC, AC=12AC=12, BC=5BC=5, and angle CC is a right angle. A semicircle is inscribed in the triangle as shown. What is the radius of the semicircle? [asy] draw((0,0)--(12,0)--(12,5)--(0,0)); draw(arc((8.67,0),(12,0),(5.33,0))); label("AA", (0,0), W); label("CC", (12,0), E); label("BB", (12,5), NE); label("1212", (6, 0), S); label("55", (12, 2.5), E);[/asy] <spanclass=′latex−bold′>(A)</span>76<spanclass=′latex−bold′>(B)</span>135<spanclass=′latex−bold′>(C)</span>5918<spanclass=′latex−bold′>(D)</span>103<spanclass=′latex−bold′>(E)</span>6013<span class='latex-bold'>(A) </span>\frac{7}{6}\qquad<span class='latex-bold'>(B) </span>\frac{13}{5}\qquad<span class='latex-bold'>(C) </span>\frac{59}{18}\qquad<span class='latex-bold'>(D) </span>\frac{10}{3}\qquad<span class='latex-bold'>(E) </span>\frac{60}{13}
AMC 8trainglescircles