Difference between revisions of "2020 OIM Problems/Problem 6"
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Latest revision as of 13:59, 14 December 2023
Problem
Let be an acute and scalene triangle. Let be the orthocenter and the circumcenter of triangle , and let be an interior point of the segment . The circumference with center and radius again intersects the lines and at points and , respectively. We denote by the point symmetrical to point with respect to the bisector of . Prove that the points , , and belong to the same circle.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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