MathDB

9.3

Part of 2006 Sharygin Geometry Olympiad

Problems(1)

equal ratios of sidelengths on similar triangles lead to collinear points

Source: Sharygin 2006 finals 9.3

9/12/2019
Triangles ABCABC and A1B1C1A_1B_1C_1 are similar and differently oriented. On the segment AA1AA_1, a point A′A' is taken such that AA′/A1A′=BC/B1C1AA' / A_1A'= BC / B_1C_1. We similarly construct B′B' and C′C'. Prove that A′,B′,C′A', B',C' lie on one straight line.
equal ratiosimilar trianglescollineargeometry