In the right triangle ABC, AC=12, BC=5, and angle C 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("A", (0,0), W); label("C", (12,0), E); label("B", (12,5), NE); label("12", (6, 0), S); label("5", (12, 2.5), E);[/asy]
<spanclass=′latex−bold′>(A)</span>67<spanclass=′latex−bold′>(B)</span>513<spanclass=′latex−bold′>(C)</span>1859<spanclass=′latex−bold′>(D)</span>310<spanclass=′latex−bold′>(E)</span>1360