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The osculating circle of a curve C at a given point P is the circle that has the same tangent as C at point P as well as the same curvature. Just as the tangent line is the ...

A circle with an arrow indicating a direction.

Let a, b, and c be the side lengths of a reference triangle DeltaABC. Now let A_b be a point on the extension of the segment CA beyond A such that AA_b=a. Similarly, define ...

Consider Kimberling centers X_(20) (de Longchamps point Z; intersection L_S intersection L_E of the Soddy line and Euler line), X_(468) (intersection L_E intersection L_O of ...

The common incircle of the medial triangle DeltaM_AM_BM_C (left figure) and the congruent triangle DeltaQ_AQ_BQ_C, where Q_i are the midpoints of the line segment joining the ...

The Stammler circle is the circumcircle of the Stammler triangle. Unexpectedly, it has center at the circumcenter O (X_3) of the reference triangle and radius 2R (Ehrmann and ...

The tangential circle of a reference triangle is the circumcircle of the tangential triangle. Its center is Kimberling center X_(26), which has center function ...

There are four completely different definitions of the so-called Apollonius circles: 1. The set of all points whose distances from two fixed points are in a constant ratio ...

The point T at which the lines through the polygon vertices of a triangle perpendicular to the corresponding sides of the first Brocard triangle, are concurrent. The Tarry ...

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 ...