Equilateral triangle Equilateral triangle In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°. It is also a regular polygon, so it is also referred to as a regular triangle. Denoting the common length of the sides of the equilateral triangle as "a", we can determine using the Pythagorean theorem that: Denoting the radius of the circumscribed circle as "R", we can determine using trigonometry that: Many of these quantities
Isodynamic point point is the intersection of three circles that intersect the circumcircle to form lenses with apex angle π/3. The angles formed by the first isodynamic point with the triangle vertices satisfy the equations formula_29, formula_30, and formula_31. Analogously, the angles formed by the second isodynamic point satisfy the equationsformula_32, formula_33, and formula_34. The pedal triangle of an isodynamic point, the triangle formed by dropping perpendiculars from formula_1 to each of the three sides of triangle formula_3, is equilateral, as is the triangle formed by reflecting formula_1 across each side of the triangle. Among all the equilateral triangles inscribed in triangle