Question 59
A diagonal in a hexagon is considered a "long" diagonal, if it divides the hexagon into two quadrilaterals. Any two long diagonals divide the hexagon into two triangles and two quadrilaterals.
We are given a convex hexagon with the property that the division into pieces by any two long diagonals always yields two isosceles triangles with sides of the hexagon as bases.
Show that such a hexagon must have a circumcircle.
We are given a convex hexagon with the property that the division into pieces by any two long diagonals always yields two isosceles triangles with sides of the hexagon as bases.
Show that such a hexagon must have a circumcircle.