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radii are equal

Source: Iranian National Olympiad (3rd Round) 2002

October 5, 2006
geometrycircumcircleratioperimetergeometry proposed

Problem Statement

Excircle of triangle ABCABC corresponding vertex AA, is tangent to BCBC at PP. APAP intersects circumcircle of ABCABC at DD. Prove r(PCD)=r(PBD)r(PCD)=r(PBD) whcih r(PCD)r(PCD) and r(PBD)r(PBD) are inradii of triangles PCDPCD and PBDPBD.
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