MathDB

Rectangle EFGH in incircle, prove that QIM = 90

Source: Taiwan 2014 TST1, Problem 3

July 18, 2014

geometryrectangleincentergeometric transformationreflectiongeometry proposed

Problem Statement

Let

ABC

be a triangle with incenter

I

, and suppose the incircle is tangent to

CA

and

AB

E

and

F

. Denote by

G

and

H

the reflections of

E

and

F

over

I

. Let

Q

be the intersection of

BC

with

GH

, and let

M

be the midpoint of

BC

. Prove that

IQ

and

IM

are perpendicular.