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Find the angle ∠MTB

Source: Kazakhstan NMO 2005 (Final round) P6

December 16, 2014

geometry proposedgeometry

Problem Statement

The line parallel to side

AC

of a right triangle

ABC

(\angle C=90^\circ)

intersects sides

AB

and

BC

at

M

and

N

, respectively, so that the

CN / BN = AC / BC = 2

. Let

O

be the intersection point of the segments

AN

and

CM

and

K

be a point on the segment

ON

such that

MO + OK = KN

. The perpendicular line to

AN

at point

K

and the bisector of triangle

ABC

of

\angle B

meet at point

T

. Find the angle

\angle MTB

.

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