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Chord problem(KgNM2011)

Source:

April 29, 2011

geometry unsolvedgeometry

Problem Statement

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

and

BC

pass through the ends of

M

and

N

of the chord

MN

. Prove that the heights of all such triangles

ABC

drawn from the vertex

C

to the side

AB

, intersect at one point.

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