Question 183
A triangle $ABC$ has an obtuse angle at $B$. The perpendicular at $B$ to $AB$ meets $AC$ at $D$, and $|CD| = |AB|$. Prove that
$$
|AD|^2 = |AB| \cdot |BC| \text{ if and only if } \angle CBD = 30^\circ.
$$
$$
|AD|^2 = |AB| \cdot |BC| \text{ if and only if } \angle CBD = 30^\circ.
$$