5

Part of 2003 Turkey Team Selection Test

Problems(1)

Reflection of midpoint of a chord over a point on diameter

Source: Turkey TST 2003 - P5

A

be a point on a circle with center

O

B

be the midpoint of

[OA]

C

D

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

OA

\widehat{CBO} = \widehat{DBA}

. Show that the reflection of the midpoint of

[CD]

B

lies on the circle.

geometrygeometric transformationreflectionparallelogramgeometry proposed