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cyclic ABCD wanted, perpendicular diagonals given

Source: Czech-Polish-Slovak Match Junior 2019, team p3 CPSJ

January 20, 2020
geometrycircumcirclecyclic quadrilateral

Problem Statement

Let ABCDABCD be a convex quadrilateral with perpendicular diagonals, such that ∠BAC=∠ADB\angle BAC = \angle ADB, ∠CBD=∠DCA\angle CBD = \angle DCA, AB=15AB = 15, CD=8CD = 8. Show that ABCDABCD is cyclic and find the distance between its circumcenter and the intersection point of its diagonals.
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