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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 ...

Two geometric figures are said to be concentric if their centers coincide. The region between two concentric circles is called an annulus. The following table summarizes some ...

The Stevanovic circle is a central circle with center X_(650), which has center function alpha_(650)=cosB-cosC, (1) It has radius (2) It has circle function ...

In any triangle, the locus of a point whose pedal triangle has a constant Brocard angle and is described in a given direction is a circle of the Schoute coaxal system.

The radical circle of three given circles is the circle having center at the radical center of the three circles and is orthogonal to all of them. (A circle with center at ...

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 ...

Given an obtuse triangle, the polar circle has center at the orthocenter H. Call H_i the feet. Then the square of the radius r is given by r^2 = HA^_·HH_A^_ (1) = HB^_·HH_B^_ ...

Given a triangle DeltaABC, construct the contact triangle DeltaT_AT_BT_C. Now extend lines parallel to the sides of the contact triangle from the Gergonne point. These ...

A central circle is a circle with trilinear equation (lalpha+mbeta+ngamma)(aalpha+bbeta+cgamma)+k(abetagamma+bgammaalpha+calphabeta)=0 such that l:m:n is a triangle center ...

The orthocentroidal circle of a triangle DeltaABC is a central circle having the segment joining the triangle centroid G and orthocenter H of DeltaABC as its diameter ...