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Find angle MXN

Source: Baltic Way 2010

November 19, 2010
geometrycircumcircleangle bisectorgeometry proposed

Problem Statement

The points MM and NN are chosen on the angle bisector ALAL of a triangle ABCABC such that ∠ABM=∠ACN=23∘\angle ABM=\angle ACN=23^{\circ}. XX is a point inside the triangle such that BX=CXBX=CX and ∠BXC=2∠BML\angle BXC=2\angle BML. Find ∠MXN\angle MXN.
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