[ Properties and characteristics of an isosceles triangle. ] [ Area of a triangle (using height and base). ]

A circle with its center on side $A C$ of the isosceles triangle $A B C (A B = B C)$ touches sides $A B$ and $B C$. Find the radius of the circle if the area of triangle $A B C$ is 25, and the ratio of the height $B D$ to side $A C$ is $3: 8$.