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TOT 117 1986 Spring S5 circumcenter lies on other circumcircle, inside #

Source:

August 29, 2019

geometrycircumcirclecircucenterparallelogram

Problem Statement

The bisector of angle

BAD

in the parallelogram

ABCD

intersects the lines

BC

and

CD

at the points

K

and

L

respectively. It is known that

ABCD

is not a rhombus. 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