Question 28
A line drawn from the vertex $A$ of an equilateral triangle $ABC$ meets the side $BC$ at $D$ and the circumcircle at $P$. Show that
$$
\frac{1}{|PD|} = \frac{1}{|PB|} + \frac{1}{|PC|}
$$
$$
\frac{1}{|PD|} = \frac{1}{|PB|} + \frac{1}{|PC|}
$$