Problem

Source: Albanian BMO TST 2010 Question 3

Tags: geometry, trapezoid, perimeter, circumcircle, geometry unsolved



Let $ K$ be the circumscribed circle of the trapezoid $ ABCD$ . In this trapezoid the diagonals $ AC$ and $ BD$ are perpendicular. The parallel sides $ AB=a$ and $ CD=c$ are diameters of the circles $ K_{a}$ and $ K_{b}$ respectively. Find the perimeter and the area of the part inside the circle $ K$, that is outside circles $ K_{a}$ and $ K_{b}$.