MathDB

2 circles

Source: Romanian IMO Team Selection Test TST 1999, problem 12; 17-th Iranian Math. Olympiad 1999/2000

May 1, 2004

geometrycircumcircleparallelogramratiogeometric transformationreflectiontrigonometry

Problem Statement

Two circles intersect at two points

A

and

B

. A line

\ell

which passes through the point

A

meets the two circles again at the points

C

and

D

, respectively. Let

M

and

N

be the midpoints of the arcs

BC

and

BD

(which do not contain the point

A

) on the respective circles. Let

K

be the midpoint of the segment

CD

. Prove that

\measuredangle MKN = 90^{\circ}

.

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