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Trapezoid inscribed in a cirlce

Source: Albanian BMO TST 2010 Question 3

March 20, 2010
geometrytrapezoidperimetercircumcirclegeometry unsolved

Problem Statement

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