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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 Euler-Gergonne-Soddy circle, a term coined here for the first time, is the circumcircle of the Euler-Gergonne-Soddy triangle. Since the Euler-Gergonne-Soddy triangle is a ...
The hypotenuse of a right triangle is the triangle's longest side, i.e., the side opposite the right angle. The word derives from the Greek hypo- ("under") and teinein ("to ...
The inner Napoleon circle, a term coined here for the first time, is the circumcircle of the inner Napoleon triangle. It has center at the triangle centroid G (and is thus ...
The point Ko of concurrence in Kosnita theorem, i.e., the point of concurrence of the lines connecting the vertices A, B, and C of a triangle DeltaABC with the circumcenters ...
The radical circle of the Lucas circles is the circumcircle of the Lucas tangents triangle. Its center has trilinear center function alpha_(1151)=2cosA+sinA (1) corresponding ...
There are two nonintersecting circles that are tangent to all three Lucas circles. (These are therefore the Soddy circles of the Lucas central triangle.) The inner one, ...
The outer Napoleon circle, a term coined here for the first time, is the circumcircle of the outer Napoleon triangle. It has center at the triangle centroid G (and is thus ...
The reflection circle, a term coined here for the first time, is the circumcircle of the reflection triangle. It has center at Kimberling center X_(195), which is the ...
The perspector of the first Morley triangle with reference triangle DeltaABC is called the second Morley center. Its triangle center function is alpha_(357)=sec(1/3A), which ...
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