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bicentric quad construction

Source: VI Soros Olympiad 1990-00 R3 9.5 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 28, 2024
geometrybicentric quadrilateral

Problem Statement

Given a circle ω\omega and three different points A,B,CA, B, C on it. Using a compass and a ruler, construct a point DD lying on the circle ω\omega such that a circle can be inscribed in the quadrilateral ABCDABCD (points AA, BB, CC, DD must be located on circle ω\omega in the indicated order).
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