Consider a right triangle with an inscribed circle. Let x and y be the lengths of the two line segments formed on the hypotenuse by the point of tangency with the circle. What interesting fact can you prove about x*y?
(In reply to A possible solution
by Old Original Oskar!)
Using some analytical geometry produces R=AB.AC/(AB+AC+BC), so XY works out to AB.AC/2, the area of the triangle.