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Weird angle condition results into concurrence

Source: BWM Germany Round 1, 2015 - Problem 3

April 8, 2015

geometryBWMGermanyrayconcurrenceangleTriangle

Problem Statement

Let

M

be the midpoint of segment

[AB]

in triangle

\triangle ABC

. Let

X

and

Y

be points such that

C

and

\angle{BYA}=\angle{MCB}

. Both points,

X

and

Y

, are on the same side as

C

with respect to line

AB

. Show that the rays

[AX

and

[BY

intersect on line

CM

.

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