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G4

Part of 2014 Balkan MO Shortlist

Problems(1)

Triangle with all coordinates rational

Source: Balkan MO 2014 G-4

6/10/2015
Let A0B0C0A_0B_0C_0 be a triangle with area equal to 2\sqrt 2. We consider the excenters A1A_1,B1B_1 and C1C_1 then we consider the excenters ,say A2,B2A_2,B_2 and C2C_2,of the triangle A1B1C1A_1B_1C_1. By continuing this procedure ,examine if it is possible to arrive to a triangle AnBnCnA_nB_nC_n with all coordinates rational.
analytic geometrygeometry