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Yatpp(yet another triangle-point problem)- parallels by p

Source: Problem 2, Brazilian MO, 1991

March 19, 2006
analytic geometrygeometryincentergeometry proposed

Problem Statement

PP is a point inside the triangle ABCABC. The line through PP parallel to ABAB meets ACAC A0A_0 and BCBC at B0B_0. Similarly, the line through PP parallel to CACA meets ABAB at A1A_1 and BCBC at C1C_1, and the line through P parallel to BC meets ABAB at B2B_2 and ACAC at C2C_2. Find the point PP such that A0B0=A1B1=A2C2A_0B_0 = A_1B_1 = A_2C_2.
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