Problem

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Tags: concurrent, geometry, circles



Three circles are constructed for the triangle ABC: the circle wA passes through the vertices B and C and intersects the sides AB and AC at points A1 and A2 respectively, the circle wB passes through the vertices A and C and intersects the sides BA and BC at the points B1 and B2, wC passes through the vertices A and B and intersects the sides CA and CB at the points C1 and C2. Let A1A2B1B2=C, A1A2C1C2=B ta B1B2C1C2=A is Prove that the perpendiculars, which are omitted from the points A,B,C to the lines BC, CA and AB respectively intersect at one point. (Rudenko Alexander)