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circular geometry configuration

Source: Moldova 2000 Grade 10 P8

April 26, 2021

geometry

Problem Statement

Two circles intersect at

M

and

N

. A line through

M

meets the circles at

A

and

B

, with

M

between

A

and

B

. Let

C

and

D

be the midpoints of the arcs

AN

and

BN

not containing

M

, respectively, and

K

and

L

be the midpoints of

AB

and

CD

, respectively. Prove that

CL=KL

.

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