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Prove four points are concyclic in an ellipse

Source: China second round 2006 p1

March 10, 2012
conicsellipsegeometry

Problem Statement

An ellipse with foci B0,B1B_0,B_1 intersects ABiAB_i at CiC_i (i=0,1)(i=0,1). Let P0P_0 be a point on ray AB0AB_0. Q0Q_0 is a point on ray C1B0C_1B_0 such that B0P0=B0Q0B_0P_0=B_0Q_0; P1P_1 is on ray B1AB_1A such that C1Q0=C1P1C_1Q_0=C_1P_1; Q1Q_1 is on ray B1C0B_1C_0 such that B1P1=B1Q1B_1P_1=B_1Q_1; P2P_2 is on ray AB0AB_0 such that C0Q1=C0Q2C_0Q_1=C_0Q_2. Prove that P0=P2P_0=P_2 and that the four points P0,Q0,Q1,P1P_0,Q_0,Q_1,P_1 are concyclic.
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