Search Results for ""

The circle H which touches the incircles I, I_A, I_B, and I_C of a circular triangle ABC and its associated triangles. It is either externally tangent to I and internally ...

The anticomplementary circle is the circumcircle of the anticomplementary triangle. It has radius R_A=2R, where R is the circumradius of the reference triangle, and center at ...

In Homogeneous coordinates (x_1,x_2,x_3), the equation of a circle C is a(x_1^2+x_2^2)+2fx_2x_3+2gx_1x_3+cx_3^2=0. The discriminant of this circle is defined as Delta=|a 0 g; ...

Given a set S of points in the plane, an enclosing circle is a circle for which all points S lie in its interior.

The hexyl circle is the circumcircle of the hexyl triangle. Amazingly, its center is at the incenter I and its radius is 2R, where R is the circumradius. Its circle function ...

The incentral circle is the circumcircle of the incentral triangle. It has radius R_I=(sqrt(abcf(a,b,c)f(b,c,a)f(c,a,b)))/(8Delta(a+b)(a+c)(b+c)), (1) where Delta is the area ...

The mixtilinear circle is the circumcircle of the mixtilinear triangle, i.e., the triangle formed by the centers of the mixtilinear incircles. Neither its center not circle ...

Morley's circle is the circumcircle of the first Morley triangle. Its center is the first Morley center, which has center function alpha_(356)=cos(1/3A)+2cos(1/3B)cos(1/3C), ...

Members of a coaxal system satisfy x^2+y^2+2lambdax+c=(x+lambda)^2+y^2+c-lambda^2=0 for values of lambda. Picking lambda^2=c then gives the two circles (x+/-sqrt(c))^2+y^2=0 ...

The symmedial circle is the circumcircle of the symmedial triangle. It has circle function l=(bc(a^4-a^2b^2-b^4-a^2c^2-b^2c^2-c^4))/(2(a^2+b^2)(a^2+c^2)(b^2+c^2)), (1) which ...