# 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, $$K_1 cdot K_3 cdot K_5=K_2 cdot K_4 cdot K_6$$