2024 SSMO Accuracy Round Problems/Problem 2

Problem

Equilateral triangle $N$ is inscribed within circle $O$ . A smaller equilateral triangle $P$ is inscribed within $N$ such that the vertices of $P$ lie on the midpoints of $N$ . The ratio of the areas between $O$ and $P$ can be expressed as $\frac{a\pi\sqrt{b}}{c},$ for relatively prime positive integers $a,c$ and squarefree $b.$ Find $a+b+c$ .

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2024 SSMO Accuracy Round Problems/Problem 2

Problem

Solution