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Intersection of lines in tangential quadrilateral lies on diameter

Source: 2021 Junior Macedonian Mathematical Olympiad P2

June 8, 2021
geometry

Problem Statement

Let ABCDABCD be a tangential quadrilateral with inscribed circle k(O,r)k(O,r) which is tangent to the sides BCBC and ADAD at KK and LL, respectively. Show that the circle with diameter OCOC passes through the intersection point of KLKL and ODOD.
Proposed by Ilija Jovchevski