Circular triangle

Examples

The intersection of three circular disks forms a convex circular triangle. For instance, a Reuleaux triangle is a special case of this construction where the three disks are centered on the vertices of an equilateral triangle, with radius equal to the side length of the triangle. However, not every convex circular triangle is formed as an intersection of disks in this way.

A circular horn triangle has all internal angles equal to zero. One way of forming some of these triangles is to place three circles, externally tangent to each other in pairs; then the central triangular region surrounded by these circles is a horn triangle. However, other horn triangles, such as the arbelos (with three collinear vertices and three semicircles as its sides) are interior to one of the three tangent circles that form it, rather than exterior to all three.

A cardioid-like circular triangle found by Roger Joseph Boscovich has three vertices equally spaced on a line, two equal semicircles on one side of the line, and a third semicircle of twice the radius on the other side of the line. The two outer vertices have the interior angle ${\displaystyle \pi }$ and the middle vertex has interior angle ${\displaystyle 2\pi }$. It has the curious property that all lines through the middle vertex bisect its perimeter.

Other circular triangles can have a mixture of convex and concave circular arc edges.