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Very similar to a Chinese TST problem

Source: Russian TST 2016, Day 11 P1 (Group A), P2 (Group B)

April 19, 2023
geometrycyclic quadrilateraltangential quadrilateral

Problem Statement

A cyclic quadrilateral ABCDABCD is given. Let II{} and JJ{} be the centers of circles inscribed in the triangles ABCABC and ADCADC. It turns out that the points B,I,J,DB, I, J, D lie on the same circle. Prove that the quadrilateral ABCDABCD is tangential.
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