angle chasing, midpoints, AM/ BC = CD/ BD 2020 Estonia Open Senior 2.5

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High School Math Grades 9-12, Ages 13-18

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#1 h Oct 18, 2020, 7:33 AM

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The bisector of the interior angle at the vertex $B$ of the triangle $ABC$ and the perpendicular line on side $BC$ passing through the vertex $C$ intersects at $D$ . Let $M$ and $N$ be the midpoints of the segments $BC$ and $BD$ , respectively, with $N$ on the side $AC$ . Find all possibilities of the angles of the triangles $ABC$ , if it is known that $\frac{| AM |}{| BC |}=\frac{|CD|}{|BD|}$ .
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