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triangle construction, given circumcircle of BHC, A, base of B altitude

Source: 2019 Oral Moscow Geometry Olympiad grades 10-11 p3

May 22, 2019
geometrycircumcircleconstruction

Problem Statement

Restore the acute triangle ABCABC given the vertex AA, the foot of the altitude drawn from the vertex BB and the center of the circle circumscribed around triangle BHCBHC (point HH is the orthocenter of triangle ABCABC).