The figure shows a triangle ABC with
the excircles EA, EB, and EC tangent to the
extension of sides at the points
A1, A2, B1, B2, C1,
and C2. Lines CA1 and BA2 meet at A3,
AB1 and CB2 meet at B3, BC1
and AC2 meet at C3. Prove that lines AA3,
BB3, and CC3 are concurrent.