Hexagon on the circumcircle of an acute triangle at the six points (including three triangle vertices) where the extended altitudes of the triangle meet the circumcircle, then the area of the hexagon is twice the area of the triangle. Let ABCDEF be a hexagon formed by six tangent lines of a conic section. Then Brianchon's theorem states that the three main diagonals AD, BE, and CF intersect at a single point. In a hexagon that is tangential to a circle and that has consecutive sides "a", "b", "c", "d", "e", and "f", If an equilateral triangle is constructed externally on each
Sum of angles of a triangle answer was proven to be positive: in other spaces (geometries) this sum can be greater or lesser, but it then must depend on the triangle. Its difference from 180° is a case of "angular defect" and serves as an important distinction for geometric systems. In Euclidean geometry, the triangle postulate states that the sum of the angles of a triangle is two right angles. This postulate is equivalent to the parallel postulate. In the presence of the other axioms of Euclidean geometry, the following statements are equivalent: The sum of the angles of a hyperbolic triangle is less than 180°.