Circular triangle Circular triangle In geometry, a circular triangle is a triangle with circular arc edges. A convex circular triangle may be constructed by three circles intersecting each other and represents the area of intersection. Its edges are all curved outwards. The sum of the internal angles of a circular triangle is greater than 180°. A Reuleaux triangle is a special case based on an equilateral triangle where the center of each arc is on the opposite vertex. A circular horn triangle is a similar concept, but represents the area interior to 3 mutually tangent circles so all of the internal angles
Langley’s Adventitious Angles the same 80-80-20 triangle but different internal angles. A quadrilateral such as BCEF in which the angles formed by the diagonals with the sides are all rational (when measured in degrees) is called an adventitious quadrangle. Numerous constructions for other adventitious quadrangles beyond the one appearing in Langley's puzzle are known. They form several infinite families and an additional set of sporadic examples. Classifying the adventitious quadrangles (which need not be convex) turns out to be equivalent to classifying all triple intersections of diagonals in regular polygons. This was solved by Gerrit Bol in 1936 (Beantwoording van prijsvraag # 17,