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Geometry . Concurrency

Source: Estonia IMO TST 1997 Day 1 P1

November 27, 2015
geometryconcurrency

Problem Statement

In a triangle ABCABC points A1,B1,C1A_1,B_1,C_1 are the midpoints of BC,CA,ABBC,CA,AB respectively,and A2,B2,C2A_2,B_2,C_2 are the midpoints of the altitudes from A,B,CA,B,C respectively. Show that the lines A1A2,B1B2,C1,C2A_1A_2,B_1B_2,C_1,C_2 are concurrent.
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