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Draw a circle that cuts three given circles perpendicularly. The solution is known as the radical circle of the given three circles. If it lies outside the three circles, ...

A construction done using only a straightedge. The Poncelet-Steiner theorem proves that all constructions possible using a compass and straightedge are possible using a ...

Cube point picking is the three-dimensional case of hypercube point picking. The average distance from a point picked at random inside a unit cube to the center is given by ...

Two circles with centers at (x_i,y_i) with radii r_i for i=1,2 are mutually tangent if (x_1-x_2)^2+(y_1-y_2)^2=(r_1+/-r_2)^2. (1) If the center of the second circle is inside ...

The line segment KO^_ joining the symmedian point K and circumcenter O of a given triangle. It is the diameter of the triangle's Brocard circle, and lies along the Brocard ...

The Lester circle is the circle on which the circumcenter C, nine-point center N, and the first and second Fermat points X and X^' lie (Kimberling 1998, pp. 229-230). Besides ...

The Yiu A-circle of a reference triangle DeltaABC is the circle passing through vertex A and the reflections of vertices B and C with respect to the opposite sides. The Yiu ...

The points of tangency t_1 and t_2 for the four lines tangent to two circles with centers x_1 and x_2 and radii r_1 and r_2 are given by solving the simultaneous equations ...

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 ...

The inverse curve of the circle with parametric equations x = acost (1) y = asint (2) with respect to an inversion circle with center (x,y) and radius R is given by x_i = ...