AHSME 1968 Problem 12

A circle passes through the vertices of a triangle with side-lengths $7\tfrac{1}{2},10,12\tfrac{1}{2}.$ The radius of the circle is: $\text{(A) } \frac{15}{4} \text{(B) } 5 \text{(C) } \frac{25}{4} \text{(D) } \frac{35}{4} \text{(E) } \frac{15\sqrt{2}}{2}$