mg.metric geometry – Equal products of triangle areas

Claim. Given hexagon circumscribed about an ellipse. Let $A_1,A_2,A_3,A_4,A_5,A_6$ be the vertices of the hexagon and let $B$ be the intersection point of its principal diagonals. Denote area of triangle $triangle A_1A_2B$ by $K_1$, area of triangle $triangle A_2A_3B$ by $K_2$,area of triangle $triangle A_3A_4B$ by $K_3$,area of triangle $triangle A_4A_5B$ by $K_4$,area of triangle $triangle A_5A_6B$ by $K_5$ and area of triangle $triangle A_1A_6B$ by $K_6$ .Then, $$K_1 cdot K_3 cdot K_5=K_2 cdot K_4 cdot K_6$$