MathDB

Midpoints of arcs reflected on sides

Source: IMOTC 2015 Practice Test 2 Problem 1

July 11, 2015

geometrycircumcirclegeometric transformationreflection

Problem Statement

Let

ABC

be a triangle in which

C

. Let

D'

be its orthocentre and

O

its circumcentre. Let

D

and

E

be respectively the midpoints of the arc

AB

not containing

C

and arc

AC

not containing

B

. Let

D'

and

E'

be respectively the reflections of

D

in

AB

and

E

in

AC

. Prove that

O, H, D', E'

lie on a circle if and only if

A, D', E'

are collinear.

Back to Problems View on AoPS