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The quadrilateral and beast

Source: RMO 2006

April 17, 2006
geometrycircumcirclegeometry proposed

Problem Statement

We have a quadrilateral ABCDABCD inscribed in a circle of radius rr, for which there is a point PP on CDCD such that CB=BP=PA=ABCB=BP=PA=AB. (a) Prove that there are points A,B,C,D,PA,B,C,D,P which fulfill the above conditions. (b) Prove that PD=rPD=r. Virgil Nicula
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