Dynamic Geometry Problem 1470: Tangential Quadrilateral, Incircles, Tangent, Parallel, Rhombus.
Let ABCD be a tangential quadrilateral and T1, T2, T3, T4 be the tangency points (see the figure below). Lines A1C2, A2C1, B1D2, B2D1 are the common external tangent to the incircles of the triangles AT1T4, BT1T2, CT2T3, DT3T4. Prove that (1) lines A1C2, T1T3, and A2C1 are parallel, similarly B1D2, T2T4, and B2D1 are parallel, (2) the quadrilateral E1E2E3E4 is a rhombus.
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