Question

Triangle KJL is inscribed in semicircle O shown below such that JK=6 and JL=11. Which of the following is closest to the radius of the semicircle?

Answer 1

Uhh, answer choices?

In any case, since $\triangle KJL$ is inscribed in a semicircle, it is a right triangle (due to the inscribed angle theorem). Thus, by the Pythagorean theorem, $KL=\sqrt{6^2+11^2}=\sqrt{157}.$ Now, the circumradius of a right triangle (the radius of the circle passing through all three of its vertices) is simply half its hypotenuse, so $OJ=OK=OL=\frac{\sqrt{157}}{2}\approx \boxed{6.265}.$