MathDB

3

Part of 2014 Taiwan TST Round 1

Problems(1)

Rectangle EFGH in incircle, prove that QIM = 90

Source: Taiwan 2014 TST1, Problem 3

7/18/2014
Let ABCABC be a triangle with incenter II, and suppose the incircle is tangent to CACA and ABAB at EE and FF. Denote by GG and HH the reflections of EE and FF over II. Let QQ be the intersection of BCBC with GHGH, and let MM be the midpoint of BCBC. Prove that IQIQ and IMIM are perpendicular.
geometryrectangleincentergeometric transformationreflectiongeometry proposed