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Find value of angle in right angled triangle

Source: Bosnia and Herzegovina TST 2007 day 2 problem 2

May 13, 2014

geometrycircumcircleangle bisectorgeometry unsolved

Problem Statement

Triangle

ABC

is right angled such that

\angle ACB=90^{\circ}

and

\frac {AC}{BC} = 2

. Let the line parallel to side

AC

intersects line segments

AB

and

BC

in

M

and

N

such that

\frac {CN}{BN} = 2

. Let

O

be the intersection point of lines

CM

and

AN

. On segment

ON

lies point

K

such that

OM+OK=KN

. Let

T

be the intersection point of angle bisector of

\angle ABC

and line from

K

perpendicular to

AN

. Determine value of

\angle MTB

.

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