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INMO 2022

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March 6, 2022
geometryincentercircumcircleINMO 2022

Problem Statement

Let DD be an interior point on the side BCBC of an acute-angled triangle ABCABC. Let the circumcircle of triangle ADBADB intersect ACAC again at E(≠A)E(\ne A) and the circumcircle of triangle ADCADC intersect ABAB again at F(≠A)F(\ne A). Let ADAD, BEBE, and CFCF intersect the circumcircle of triangle ABCABC again at D1(≠A)D_1(\ne A), E1(≠B)E_1(\ne B) and F1(≠C)F_1(\ne C), respectively. Let II and I1I_1 be the incentres of triangles DEFDEF and D1E1F1D_1E_1F_1, respectively. Prove that E,F,I,I1E,F, I, I_1 are concyclic.
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