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Perpendiculars from midpoints to incentral triangle

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October 10, 2010
geometry unsolvedgeometry

Problem Statement

The circle inscribed in the triangle A1A2A3A_1A_2A_3 is tangent to its sides A1A2,A2A3,A3A1A_1A_2, A_2A_3, A_3A_1 at points T1,T2,T3T_1, T_2, T_3, respectively. Denote by M1,M2,M3M_1, M_2, M_3 the midpoints of the segments A2A3,A3A1,A1A2A_2A_3, A_3A_1, A_1A_2, respectively. Prove that the perpendiculars through the points M1,M2,M3M_1, M_2, M_3 to the lines T2T3,T3T1,T1T2T_2T_3, T_3T_1, T_1T_2 meet at one point.
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