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The second Brocard circle is the circle having center at the circumcenter O of the reference triangle and radius R_B = sqrt(1-4sin^2omega)R (1) = (2) where R is the ...

Let I_A, I_B, and I_C be the vertices of the inner Soddy triangle, and also let E_A, E_B, and E_C be the pairwise contact points of the three tangent circles. Then the lines ...

The second Steiner circle (a term coined here for the first time) is the circumcircle of the Steiner triangle DeltaS_AS_BS_C. Its center has center function ...

Half a circle. The area of a semicircle of radius r is given by A = int_0^rint_(-sqrt(r^2-x^2))^(sqrt(r^2-x^2))dxdy (1) = 2int_0^rsqrt(r^2-x^2)dx (2) = 1/2pir^2. (3) The ...

Given a triangle DeltaABC with inner and outer Soddy centers S and S^', respectively, the inner Soddy triangle DeltaPQR (respectively, outer Soddy triangle DeltaP^'Q^'R^') is ...

A stadium, also called a discorectangle, obround, or sausage body, is a geometric figure consisting of a rectangle with top and bottom lengths a whose ends are capped off ...

The Stammler hyperbola of a triangle is the Feuerbach hyperbola of its tangential triangle, and its center is the focus of the Kiepert parabola, which is Kimberling center ...

The Steiner circle is the central circle with center at the nine-point center X_5 and radius R_S=3/2R, where R is the circumradius of the reference triangle. It is the ...

The tangential circle of a reference triangle is the circumcircle of the tangential triangle. Its center is Kimberling center X_(26), which has center function ...

A toric section is a curve obtained by slicing a torus (generally a horn torus) with a plane. A spiric section is a special case of a toric section in which the slicing plane ...