Geometry test pending from Q2

Q1. Let ABC be a given equilateral triangle. Denote the mid-points of sides BC, CA, AB respectively by A1, B1, C1. Three distinct parallel lines p, q,r are drawn through A1, B1, C1, respectively. Line p cuts B1C1 at A2; line q cuts C1A1 at B2; line r cuts A1B1 at C2. Prove that the lines AA2, BB2, CC2 are concurrent.

S1.


 

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