MathDB

Reflection of midpoint of a chord over a point on diameter

Source: Turkey TST 2003 - P5

April 6, 2013

geometrygeometric transformationreflectionparallelogramgeometry proposed

Problem Statement

Let

A

be a point on a circle with center

O

and

B

be the midpoint of

[OA]

. Let

C

and

D

be points on the circle such that they lie on the same side of the line

OA

and

\widehat{CBO} = \widehat{DBA}

. Show that the reflection of the midpoint of

[CD]

over

B

lies on the circle.