We have length of three sides which are $5,6,7$. How can the radius be found? Is there any easy way to find that? If the angles were there, it would be found from, $$ r = c \cdot\frac{sin\frac{ A}{2} \cdot sin\frac{B}{2}}{cos \frac{C}{2}} $$
I can't find a simple way for it.
The forumla is $$R = {abc\over 4A}$$
where $A = \sqrt{s(s-a)(s-b)(s-b)}$ is area of triangle and $s$ is half of a perimeter of triangle.