Question 15
Let $ABC$ be a planar triangle. Let $\lambda \ge 0$. Define the point $D(\lambda)$ on the side $BC$ so that $D(\lambda)$ divides $BC$ in the ratio $c^\lambda : b^\lambda$. Prove that
$$
|AD(\lambda)| \le |AD(2 - \lambda)| \quad \text{iff} \quad \lambda \ge 1.
$$
$$
|AD(\lambda)| \le |AD(2 - \lambda)| \quad \text{iff} \quad \lambda \ge 1.
$$