circumcenter is midpoint of segment of incenter-orthocenter of another triangle
Source: Sharygin 2006 X-XI CR 19
August 24, 2019
geometryincentermidpointsperpendicularCircumcenterorthocenter
Problem Statement
Through the midpoints of the sides of the triangle , straight lines are drawn perpendicular to the bisectors of the opposite angles of the triangle. These lines formed a triangle . Prove that the center of the circle circumscribed about is in the midpoint of the segment formed by the center of the inscribed circle and the intersection point of the heights of triangle .