Solution: For a right triangle, the inradius $ r = \fraca + b - c2 $, where $ c $ is the hypotenuse. Let $ a $ and $ b $ be the legs. Then $ r = \fraca + b - 252 = 6 \Rightarrow a + b = 37 $. The area of the triangle is $ \fracab2 $, and the inradius formula $ r = \fraca + b - c2 $ gives consistency. Using $ a^2 + b^2 = 625 $ and $ a + b = 37 $, solve for $ ab $: $ (a + b)^2 = 1369 = a^2 + b^2 + 2ab = 625 + 2ab \Rightarrow ab = 372 $. Area $ = 186 \, \textm^2 $. Circle area $ \pi r^2 = 36\pi $. Ratio $ \frac36\pi186 = \boxed\frac6\pi31 $. - Nelissen Grade advocaten