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Specifying three sides uniquely determines a triangle whose area is given by Heron's formula, K=sqrt(s(s-a)(s-b)(s-c)), (1) where s=1/2(a+b+c) (2) is the semiperimeter of the ...

The point of coincidence of P and P^' in Fagnano's theorem.

The radical line, also called the radical axis, is the locus of points of equal circle power with respect to two nonconcentric circles. By the chordal theorem, it is ...

Specifying three angles A, B, and C does not uniquely define a triangle, but any two triangles with the same angles are similar. Specifying two angles of a triangle ...

Specifying two angles A and B and a side a opposite A uniquely determines a triangle with area K = (a^2sinBsinC)/(2sinA) (1) = (a^2sinBsin(pi-A-B))/(2sinA). (2) The third ...

Specifying two adjacent angles A and B and the side between them c uniquely (up to geometric congruence) determines a triangle with area K=(c^2)/(2(cotA+cotB)). (1) The angle ...

Specifying two sides and the angle between them uniquely (up to geometric congruence) determines a triangle. Let c be the base length and h be the height. Then the area is ...

The Balthasart projection is a cylindrical equal-area projection that uses a standard parallel of phi_s=50 degrees.

The extremities of parallel radii of two circles are called homologous with respect to the similitude center collinear with them.

Nonconcurrent triangles with parallel sides are always homothetic. Homothetic triangles are always perspective triangles. Their perspector is called their homothetic center.