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2022 MMATHS Individual p12 - Geometry, where art thou?

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October 1, 2023
geometryMMATHS

Problem Statement

Let triangle ABCABC with incenter II satisfy AB=10AB = 10, BC=21BC = 21, and CA=17CA = 17. Points DD and E lie on side BCBC such that BD=4BD = 4, DE=6DE = 6, and EC=11EC = 11. The circumcircles of triangles BIEBIE and CIDCID meet again at point PP, and line IPIP meets the altitude from AA to BCBC at XX. Find (DXā‹…EX)2(DX \cdot EX)^2.
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