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Part of 2011 Kyrgyzstan National Olympiad

Problems(1)

Chord problem(KgNM2011)

Source:

For a given chord

MN

of a circle discussed the triangle

ABC

, whose base is the diameter

AB

of this circle,which do not intersect the

MN

, and the sides

AC

BC

pass through the ends of

M

N

MN

. Prove that the heights of all such triangles

ABC

drawn from the vertex

C

AB

, intersect at one point.

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