Question 10
II 4 (FIN 3), IMO2
Let $\triangle ABC$ be a triangle. Prove that there exists a point $D$ on the side $AB$ such that $CD$ is the geometric mean of $AD$ and $BD$ if and only if $\sqrt{\sin A\sin B}\le\sin\frac C2$.
Let $\triangle ABC$ be a triangle. Prove that there exists a point $D$ on the side $AB$ such that $CD$ is the geometric mean of $AD$ and $BD$ if and only if $\sqrt{\sin A\sin B}\le\sin\frac C2$.