parallel and locus of midpoints wanted, as a point moves along a long arc
Source: Czech-Polish-Slovak Junior Match 2012, Team p2 CPSJ
March 12, 2020
midpointparallelgeometryLocusarc
Problem Statement
On the circle , the points are given, while is not the diameter of the circle . Point moves along the long arc of circle so that the triangle is acute. Let be the feet of the altitudes from respectively. Let be the projection of point on line and be the projection of point on line .
(a) Prove that the lines and are parallel.
(b) Determine the set of midpoints of segment while along all allowable positions of point .