Question 133
Consider three collinear points $B$, $C$ and $D$ such that $C$ lies between $B$ and $D$. Let $A$ be a point not on the line $BD$ such that $AB = AC = CD$.
a. If $\angle BAC = 36^{\circ}$, verify that
$$
\frac{1}{CD} - \frac{1}{BD} = \frac{1}{CD + BD}
$$
b. Now suppose that
$$
\frac{1}{CD} - \frac{1}{BD} = \frac{1}{CD + BD}
$$
holds. Verify that $\angle BAC = 36^{\circ}$.
a. If $\angle BAC = 36^{\circ}$, verify that
$$
\frac{1}{CD} - \frac{1}{BD} = \frac{1}{CD + BD}
$$
b. Now suppose that
$$
\frac{1}{CD} - \frac{1}{BD} = \frac{1}{CD + BD}
$$
holds. Verify that $\angle BAC = 36^{\circ}$.