# #30 of Sept 2016 Grade 10 CSAT (Korean SAT) Mock Test

Geometry Level 5

I've drawn 2 triangles with one inscribed in the other, i.e. with the vertices of the smaller triangle lying on different sides of the large triangle. Given that the large triangle has side lengths $$3\sqrt{2},\, 4,$$ and $$\sqrt{10},$$ as shown in the figure, let $$P$$ denote the minimum possible perimeter of the smaller triangle.

If $$P^2$$ can be expressed as $$\frac MN,$$ where $$M$$ and $$N$$ are coprime positive integers, find $$M+N.$$

This problem is a part of <Grade 10 CSAT Mock Test> series.

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