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PAMO Problem 6: Two tangent circles

Source: 2021 Pan-African Mathematics Olympiad, Problem 6

May 24, 2021
geometrytangentcircumcircletrapezoidPAMO

Problem Statement

Let ABCDABCD be a trapezoid which is not a parallelogram, such that ADAD is parallel to BCBC. Let O=BD∩ACO=BD\cap AC and SS be the second intersection of the circumcircles of triangles AOBAOB and DOCDOC. Prove that the circumcircles of triangles ASDASD and BSCBSC are tangent.
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