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N satisfies ∠ NBA =∠ BAM and ∠ NCA = ∠ CAM

Source: Romanian TST 2000

February 18, 2011
geometrycircumcirclegeometry proposed

Problem Statement

Let ABCABC be an acute-angled triangle and MM be the midpoint of the side BCBC. Let NN be a point in the interior of the triangle ABCABC such that ∠NBA=∠BAM\angle NBA=\angle BAM and ∠NCA=∠CAM\angle NCA=\angle CAM. Prove that ∠NAB=∠MAC\angle NAB=\angle MAC.
Gabriel Nagy
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