IMO 1984 LL BUL9
The circle inscribed in the triangle A1A2A3 is tangent to
IMO 1984 LL BUL9
Origin: BUL
Problem
The circle inscribed in the triangle A1A2A3 is tangent to its sides A1A2, A2A3, A3A1 at points T1, T2, T3, respectively. Denote by M1, M2, M3 the midpoints of the segments A2A3, A3A1, A1A2, respec- tively. Prove that the perpendiculars through the points M1, M2, M3 to the lines T2T3, T3T1, T1T2 meet at one point.