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Proving Collinearity in a Triangle

Source: Mathematics Regional Olympiad of Mexico Southeast 2023 P2

October 8, 2023
geometrycollinear

Problem Statement

Let ABCABC be an acute-angled triangle, DD be the foot of the altitude from AA, the circle with diameter ADAD intersect ABAB at FF and ACAC at EE. Let PP be the orthocenter of triangle AEFAEF and OO be the circumcenter of ABCABC. Prove that A,P,A, P, and OO are collinear.
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