Question 81
$ABC$ is a triangle, $G$ its centroid and $A'$, $B'$, $C'$ the midpoints of its sides $BC$, $CA$, $AB$, respectively. Prove that if the quadrilateral $AC'GB'$ is cyclic then
$$
AB \cdot CC' = AC \cdot BB'.
$$
$$
AB \cdot CC' = AC \cdot BB'.
$$