Ex. 118. A circle with center on side $AB$ of triangle $ABC$ touches sides $AC$ and $BC$. Find the radius of the circle, given that it is expressed as an integer, and sides $AC$ and $BC$ are equal to 5 and 3.
Ex. 118. Answer: $r=1$. Solution. By equating the expressions for the area of triangle $ABC$, we get that $\frac{a+b}{2} r=\frac{a b}{2} \sin C$. From this, it follows that $r=\frac{a b}{a+b} \sin C$. In our case, $r=\frac{15}{8} \sin C$. If $r \geq 2$, then $\sin C>1$. This solves the problem.