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Tangents AA',BB',CC',DD' form p with axis of symmetry

Source: Romanian TST 2001

January 16, 2011
symmetrygeometry proposedgeometry

Problem Statement

The vertices A,B,CA,B,C and DD of a square lie outside a circle centred at MM. Let AA′,BB′,CC′,DD′AA',BB',CC',DD' be tangents to the circle. Assume that the segments AA′,BB′,CC′,DD′AA',BB',CC',DD' are the consecutive sides of a quadrilateral pp in which a circle is inscribed. Prove that pp has an axis of symmetry.
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