5. Points $M, N, P$ are the feet of the altitudes dropped from the vertices of triangle $A B C$ with angles $37.5^{0}, 67.5^{0}, 75^{0}$ to its sides. Find the ratio of the areas of triangles $M N P$ and $A B C$.
Answer: $(2 \sqrt{3}+3 \sqrt{2}-\sqrt{6}-4): 8$.

## Final round of the "Rosatom" Olympiad, 10th grade, CIS, February 2020

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