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5

Part of 2007 Bosnia Herzegovina Team Selection Test

Problems(1)

Find value of angle in right angled triangle

Source: Bosnia and Herzegovina TST 2007 day 2 problem 2

5/13/2014
Triangle ABCABC is right angled such that ∠ACB=90∘\angle ACB=90^{\circ} and ACBC=2\frac {AC}{BC} = 2. Let the line parallel to side ACAC intersects line segments ABAB and BCBC in MM and NN such that CNBN=2\frac {CN}{BN} = 2. Let OO be the intersection point of lines CMCM and ANAN. On segment ONON lies point KK such that OM+OK=KNOM+OK=KN. Let TT be the intersection point of angle bisector of ∠ABC\angle ABC and line from KK perpendicular to ANAN. Determine value of ∠MTB\angle MTB.
geometrycircumcircleangle bisectorgeometry unsolved