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MathNet 2026 — Part 08 Question 71

Math Olympiad Vault · MathNet 2026 — Part 08

Question 71

Let $ABC$ be a triangle, and let $M$ and $N$ be the respective midpoints of $AB$ and $AC$. Suppose that
$$
\frac{CM}{AC} = \frac{\sqrt{3}}{2}
$$
Prove that
$$
\frac{BN}{AB} = \frac{\sqrt{3}}{2}
$$