Lines parallel to UV, UW, VW concurrent
Source: 2024 Israel National Olympiad (Gillis) P4
December 7, 2023
geometryconcurrenceTriangleCircumcentergeometric transformationreflection
Problem Statement
Acute triangle is inscribed in a circle with center . The reflections of across the three altitudes of the triangle are called , , : over the altitude from , over the altitude from , and over the altitude from .
Let be a line through parallel to , and define , similarly. Prove that the three lines , , are concurrent.