If a ball is rolled into the corner of a room how far is its centre
from the corner?
Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.
This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the triangle.
Here is a hint for this tough nut. Just think about the angle
between a chord and a tangent to a circle and think about cyclic