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Members of a coaxal system satisfy x^2+y^2+2lambdax+c=(x+lambda)^2+y^2+c-lambda^2=0 for values of lambda. Picking lambda^2=c then gives the two circles (x+/-sqrt(c))^2+y^2=0 ...

For two lines in the plane with endpoints (x_1,x_2) and (x_3,x_4), the angle between them is given by costheta=((x_2-x_1)·(x_4-x_3))/(|x_2-x_1||x_4-x_3|). (1) The angle theta ...

An umbilic point, also called simply an umbilic, is a point on a surface at which the curvature is the same in any direction.

A prime-distance graph is a distance graph with distance set given by the set of prime numbers.

Let D be a set of positive numbers containing 1, then the D-distance graph X(D) on a nonempty subset X of Euclidean space is the graph with vertex set X and edge set ...

The point F at which the incircle and nine-point circle are tangent. It has triangle center function alpha=1-cos(B-C) (1) and is Kimberling center X_(11). If F is the ...

A Cevian point P is point with respect to which a set of Cevians of a triangle are taken. Connecting the endpoints of the Cevians through a point P gives the so-called Cevian ...

The graph distance matrix, sometimes also called the all-pairs shortest path matrix, is the square matrix (d_(ij)) consisting of all graph distances from vertex v_i to vertex ...

For n points in the plane, there are at least N_1=sqrt(n-3/4)-1/2 different distances. The minimum distance can occur only <=3n-6 times, and the maximum distance can occur ...

While the pedal point, Cevian point, and even pedal-Cevian point are commonly used concepts in triangle geometry, there seems to be no established term to describe the ...