MathDB

Centre of (CKL) lies on (BCD)

Source: South Africa 1999

September 30, 2005

geometryparallelogramcircumcircletrigonometryratiogeometric transformationrotation

Problem Statement

The bisector of

\angle{BAD}

in the parallellogram

ABCD

intersects the lines

BC

and

CD

at the points

K

and

L

respectively. Prove that the centre of the circle passing through the points

C,\ K

and

L

lies on the circle passing through the points

B,\ C

and

D