Inscribed in a Circle

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The area of a square inscribed in a circle with a unit radius is, satisfyingly, $2$.

What is the area of a regular hexagon inscribed in a circle with a unit radius?

Circle within a hexagon

What is the area of an equilateral triangle inscribed in a circle with a unit radius?

Triangle within a circle


Published February 2004.