The radius can be found with the Pythagorean theorem. Assuming r is the radius, 14²+r²=17². Multiply it out to 196+r²=289. Subtract 196 from both sides and you're left with r²=93. So, r=√93, or about 9.6 to the nearest tenth.
Since the radius of that circle is side AB of the triangle, and the triangle is a right triangle, we can use pythagorean theorem. A (squared) + B (squared) = C (squared. We have one of the legs and the hypotenuse, so we just have to solve for the other leg. 17 squared - 14 squared is 93. The square root of 93 is 9.6. So the radius would be 9.6.
