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AD=AB+CD, tangent circle to 3 sides, cyclic (2020 Novosibirsk Oral Geo Oly 9.7)

Source:

May 24, 2021
geometryCyclicTangents

Problem Statement

The quadrilateral ABCDABCD is known to be inscribed in a circle, and that there is a circle with center on side ADAD tangent to the other three sides. Prove that AD=AB+CDAD = AB + CD.