# A geometry problem by Neel Khare

Geometry Level 4

Consider a triangle $$ABC$$ with $$N$$ as the center of its nine point circle, and $$R$$ as its circumradius.

Let $$a,b,c$$ denote the side opposite to the vertices $$A,B,C$$, respectively.

With $$AN = \sqrt{12}$$ and $$R = \sqrt{13}$$.

If the product of length $$b\times c$$ is 35, what is the value of $$a^2$$?

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