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The Brocard circle, also known as the seven-point circle, is the circle having the line segment connecting the circumcenter O and symmedian point K of a triangle DeltaABC as ...

Draw antiparallels through the symmedian point K. The points where these lines intersect the sides then lie on a circle, known as the cosine circle (or sometimes the second ...

A great circle is a section of a sphere that contains a diameter of the sphere (Kern and Bland 1948, p. 87). Sections of the sphere that do not contain a diameter are called ...

Consider a unit circle and a radiant point located at (mu,0). There are four different regimes of caustics, illustrated above. For radiant point at mu=infty, the catacaustic ...

A circle having a given number of lattice points on its circumference. The Schinzel circle having n lattice points is given by the equation {(x-1/2)^2+y^2=1/45^(k-1) for n=2k ...

Given a circle expressed in trilinear coordinates by a central circle is a circle such that l:m:n is a triangle center and k is a homogeneous function that is symmetric in ...

In the figure above with tangent line PT and secant line PA, (PA)/(PT)=(PT)/(PB) (1) (Jurgensen et al. 1963, p. 346). The line tangent to a circle of radius a centered at ...

For every positive integer n, there exists a circle which contains exactly n lattice points in its interior. H. Steinhaus proved that for every positive integer n, there ...

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 ...

The nine-point circle, also called Euler's circle or the Feuerbach circle, is the circle that passes through the perpendicular feet H_A, H_B, and H_C dropped from the ...