A triangle is drawn with its vertices on the circle $C$ such that one of its sides is a diameter of $C$ and the other two sides have their lengths in the ratio $a: b$. If the radius of the circle is $r$, then the area of the triangle is
- $\frac{2 a b r^{2}}{a^{2}+b^{2}}$
- $\frac{a b r^{2}}{a^{2}+b^{2}}$
- $\frac{a b r^{2}}{2\left(a^{2}+b^{2}\right)}$
- $\frac{4 a b r^{2}}{a^{2}+b^{2}}$