Geometry · Isosceles triangle · Congruent triangles · Angle chasing · Auxiliary point
Let \(ABC\) be an isosceles triangle with \(AB = BC\). A point \(M\) is chosen inside it so that
\[ \angle AMC = 2 \angle ABC , \]
and a point \(N\) on the segment \(AM\) satisfies \(\angle BNM = \angle ABC\). Prove that
\[ BN = CM + MN . \]
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Serbian Regional Competition 2011, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source