1.18. The lengths of two sides of a triangle are $a$, and the length of the third side is $b$. Calculate the radius of its circumscribed circle.
1.18. Let $O$ be the center of the circumscribed circle of isosceles triangle $ABC$, $B_{1}$ the midpoint of the base $AC$, and $A_{1}$ the midpoint of the lateral side $BC$. Since $\triangle B O A_{1} \sim \triangle B C B_{1}$, then $B O: B A_{1}=B C: B B_{1}$, which means $R=B O=$ $=a^{2} / \sqrt{4 a^{2}-b^{2}}$.