MathDB

19

Part of 2006 Sharygin Geometry Olympiad

Problems(1)

circumcenter is midpoint of segment of incenter-orthocenter of another triangle

Source: Sharygin 2006 X-XI CR 19

8/24/2019
Through the midpoints of the sides of the triangle TT, straight lines are drawn perpendicular to the bisectors of the opposite angles of the triangle. These lines formed a triangle T1T_1. Prove that the center of the circle circumscribed about T1T_1 is in the midpoint of the segment formed by the center of the inscribed circle and the intersection point of the heights of triangle TT.
geometryincentermidpointsperpendicularCircumcenterorthocenter