Question 4
In the diagram below, points $A_1$, $A_2$, $A_3$, $A_4$, $A_5$ lie on the circumference of a unit circle and
$$\angle A_5A_2A_4=\angle A_1A_3A_5=\angle A_2A_4A_1=\angle A_3A_5A_2=30^\circ.$$
Let $A_2A_4$ and $A_3A_5$, $A_3A_5$ and $A_4A_1$, $A_4A_1$ and $A_5A_2$, $A_5A_2$ and $A_1A_3$ intersect at points $B_1$, $B_2$, $B_3$, $B_4$, $B_5$, respectively. Find the area, in square units, of the pentagon $B_1B_2B_3B_4B_5$.
**Source note.** The printed sentence lists four pairs of chords but five intersection labels. The supplied diagram identifies the remaining point as $B_5=A_1A_3\cap A_2A_4$; the original sentence and diagram are preserved above.
$$\angle A_5A_2A_4=\angle A_1A_3A_5=\angle A_2A_4A_1=\angle A_3A_5A_2=30^\circ.$$
Let $A_2A_4$ and $A_3A_5$, $A_3A_5$ and $A_4A_1$, $A_4A_1$ and $A_5A_2$, $A_5A_2$ and $A_1A_3$ intersect at points $B_1$, $B_2$, $B_3$, $B_4$, $B_5$, respectively. Find the area, in square units, of the pentagon $B_1B_2B_3B_4B_5$.
**Source note.** The printed sentence lists four pairs of chords but five intersection labels. The supplied diagram identifies the remaining point as $B_5=A_1A_3\cap A_2A_4$; the original sentence and diagram are preserved above.