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Two excircles and points of tangency. Three collinear points wanted.

Source: St. Petersburg MO 2000, 10th grade, P6

April 22, 2023
geometryexcirclecollinearity

Problem Statement

One of the excircles of triangle ABCABC is tangent to the side ABAB and to the extensions of sides CACA and CBCB at points C1C_1, B1B_1 and A1A_1 respectively. Another excircle is tangent to side ABAB and to the extensions of sides BABA and BCBC at points B2B_2, C2C_2 and A2A_2 respectively. Line A1B1A_1B_1 and A2B2A_2B_2 intersect at point PP,. lines A1C1A_1C_1 and A2C2A_2C_2 intersect at point QQ. Prove that the points AA, PP, QQ are collinear
[I]Proposed by S. Berlov
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