Question 30
Consider a convex pentagon $A_0A_1A_2A_3A_4$ so that the rays ($A_iA_{i+1}$ and ($A_{i+3}A_{i+2}$ meet at $B_{i+4}$, for each $i = 0, 1, 2, 3, 4$ – indices are considered modulo 5. Show that
$$
\prod_{i=0}^{4} A_i B_{i+3} = \prod_{i=0}^{4} A_i B_{i+2}.
$$
$$
\prod_{i=0}^{4} A_i B_{i+3} = \prod_{i=0}^{4} A_i B_{i+2}.
$$