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locus of midpoints of altitudes wanted, fixed circle and point given

Source: 2018 Oral Moscow Geometry Olympiad grades 8-9 p5

July 25, 2019
geometryLocusfixedmidpointsorthocenter

Problem Statement

The circle circumscribed about an acute triangle ABCABC and the vertex CC are fixed. Orthocenter HH moves in a circle with center at point CC. Find the locus of the midpoints of the segments connecting the feet of altitudes drawn from vertices AA and BB.
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