AIME I 2025 (Problem 6)

Plane GeometryMedium

An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is

3

, and the area of the trapezoid is

72

. Let the parallel sides of the trapezoid have lengths

r

and

s

, with

r\ne s

. Find

r^2+s^2