Question 31
A square and an equilateral triangle are inscribed to a circle. The seven vertices form a convex heptagon $H$ that is inscribed to the circle. (As a special case $H$ can be a hexagon if a vertex of the square coincides with a vertex of the triangle.)
For which positions of the triangle relative to the square does $H$ have the biggest resp. smallest possible values?
For which positions of the triangle relative to the square does $H$ have the biggest resp. smallest possible values?