MathDB
3 cockroaches run along a circle in different speeds, locus of centroids

Source: 2021 Sharygin Finals grade VIII p3

August 1, 2021
LocusCentroidgeometryspeed

Problem Statement

Three cockroaches run along a circle in the same direction. They start simultaneously from a point SS. Cockroach AA runs twice as slow than BB, and thee times as slow than CC. Points X,YX, Y on segment SCSC are such that SX=XY=YCSX = XY =YC. The lines AXAX and BYBY meet at point ZZ. Find the locus of centroids of triangles ZABZAB.
Back to ProblemsView on AoPS