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P_1 Q_1 R_1 is congruent to triangle P_2 Q_2 R_2

Source: China TST 1989, problem 4

June 27, 2005
geometrycircumcirclegeometric transformationrotationcongruent trianglescyclic quadrilateral

Problem Statement

Given triangle ABCABC, squares ABEF,BCGH,CAIJABEF, BCGH, CAIJ are constructed externally on side AB,BC,CAAB, BC, CA, respectively. Let AH∩BJ=P1AH \cap BJ = P_1, BJ∩CF=Q1BJ \cap CF = Q_1, CF∩AH=R1CF \cap AH = R_1, AG∩CE=P2AG \cap CE = P_2, BI∩AG=Q2BI \cap AG = Q_2, CE∩BI=R2CE \cap BI = R_2. Prove that triangle P1Q1R1P_1 Q_1 R_1 is congruent to triangle P2Q2R2P_2 Q_2 R_2.
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