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locus of (a) orthocenters (b) centroids (c) circumcenters

Source: Sharygin 2005 VIII-X CR 5

August 18, 2019
geometryLocusorthocenterCircumcenterCentroidcircumcircle

Problem Statement

There are two parallel lines p1p_1 and p2p_2. Points AA and BB lie on p1p_1, and CC on p2p_2. We will move the segment BCBC parallel to itself and consider all the triangles AB′C′AB'C ' thus obtained. Find the locus of the points in these triangles: a) points of intersection of heights, b) the intersection points of the medians, c) the centers of the circumscribed circles.
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