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Guessing Point is Hard

Source: IMO Shortlist 2023 G5

July 17, 2024
geometryIMO ShortlistAZE IMO TST

Problem Statement

Let ABCABC be an acute-angled triangle with circumcircle ω\omega and circumcentre OO. Points D≠BD\neq B and E≠CE\neq C lie on ω\omega such that BD⊥ACBD\perp AC and CE⊥ABCE\perp AB. Let COCO meet ABAB at XX, and BOBO meet ACAC at YY.
Prove that the circumcircles of triangles BXDBXD and CYECYE have an intersection lie on line AOAO.
Ivan Chan Kai Chin, Malaysia
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