MathDB

5

Part of 2005 Sharygin Geometry Olympiad

Problems(1)

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

Source: Sharygin 2005 VIII-X CR 5

8/18/2019
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.
geometryLocusorthocenterCircumcenterCentroidcircumcircle