A geometry problem by Neel Khare

Geometry Level 5

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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