$y-x=0$ is the equation of a side of a $\triangle A B C$. The orthocentre and circumcentre of the $\triangle A B C$ are respectively $(5,8)$ and $(2,3)$. The reflection of orthocentre with respect to any side of the triangle lies on its circumcircle. Then, the radius of the circumcircle of the triangle is

If $a=3, b=5, c=7$ are the sides of a $\triangle A B C$, then $\cot A+\cot B+\cot C=$

Let $p_1, p_2$ and $p_3$ be the altitudes of a $\triangle A B C$ drawn through the vertices $A, B$ and $C$ respectively. If $r_1=4$, $r_2=6, r_3=12$ are the ex-radii of $\triangle A B C$, then $\frac{1}{p_1^2}+\frac{1}{p_2^2}+\frac{1}{p_3^2}=$

If $a=3, b=5, c=7$ are the sides of a $\triangle A B C$, then its circumradius is