[ Properties and characteristics of an isosceles triangle. ]

In an isosceles triangle, the center of the inscribed circle divides the height in the ratio $12: 5$, and the lateral side is equal to 60. Find the base.
Let $CM$ be the altitude of the given triangle $ABC$, $AC=BC=60$, $O$ be the center of the inscribed circle. It is clear that $AM$ $<MC$. Since $AO$ is the bisector of angle $BAC$, then $AM=5/12 AC=25$, and $AB=2 AM=50$.

## Answer

50.