MathDB

locus of the orthocenter of the touchpoints of the incircle

Source: Hungary-Israel Binational 2000 day P3

September 27, 2017

geometryorthocenterincircle

Problem Statement

Let

{ABC}

be a non-equilateral triangle. The incircle is tangent to the sides

{BC,CA,AB}

{A_1,B_1,C_1}

, respectively, and M is the orthocenter of triangle

{A_1B_1C_1}

. Prove that

{M}

lies on the line through the incenter and circumcenter of

{\vartriangle ABC}