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Show that \angle MKN =\pi/2

Source: ARMO 1997, 10.3

April 20, 2013

geometry proposedgeometry

Problem Statement

Two circles intersect at

A

and

B

. A line through

A

meets the first circle again at

C

and the second circle again at

D

. Let

M

and

N

be the midpoints of the arcs

BC

and

BD

not containing

A

, and let

K

be the midpoint of the segment

CD

. Show that

\angle MKN =\pi/2

. (You may assume that

C

and

D

lie on opposite sides of

A

.) D. Tereshin

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