Angle trisection with coefficients in the field generated by these numbers. Therefore, any number that is constructible by a sequence of steps is a root of a minimal polynomial whose degree is a power of two. Note also that radians (60 degrees, written 60°) is constructible. The argument below shows that it is impossible to construct a 20° angle. This implies that a 60° angle cannot be trisected, and thus that an arbitrary angle cannot be trisected. Denote the set of rational numbers by . If 60° could be trisected, the degree of a minimal polynomial of over would be a power
Triangle (in fact, this formula holds for "all" tangential polygons), and where formula_59 are the radii of the excircles tangent to sides "a, b, c" respectively. We also have and for circumdiameter "D"; and for angle α ≠ 90°. The area can also be expressed as In 1885, Baker gave a collection of over a hundred distinct area formulas for the triangle. These include: for circumradius (radius of the circumcircle) "R", and The area "T" of any triangle with perimeter "p" satisfies with equality holding if and only if the triangle is equilateral. Other upper bounds on the area "T" are