Summer Problem Solving Marathon Solution #34

When a right triangle is inscribed in a circle, its hypotenuse is a diameter of the circle. Thus the hypotenuse of the triangle is 14. Since the triangle is a 3:4:5 right triangle, its legs are then 42/5 and 56/5. The area of the triangle is then 1/2(42/5)(56/5) = 1176/25 = 47.04.