smc

The triangle that goes through all the vertices of the triangle is the circumcircle of the triangle. $(7\frac{1}{2}{)}^2+10^2=(12\frac{1}{2}{)}^2$, so the triangle is a right triangle.The radius of a circumcircle of a right triangle is half the hypotenuse. $\frac{1}{2}\cdot \frac{25}{2}=\frac{25}{4}⟹$ $\boxed{\frac{25}{4}}$