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Let A_1, B_2, C_1, A_2, and B_1 be five points determining a conic. Then the conic is the locus of the point C_2=A_1(L·C_1A_2)·B_1(L·C_1B_2), where L is a line through the ...

Pick a point O in the interior of a quadrilateral which is not a parallelogram. Join this point to each of the four vertices, then the locus of points O for which the sum of ...

There are several definitions of a ray. When viewed as a vector, a ray is a vector AB^-> from a point A to a point B. In geometry, a ray is usually taken as a half-infinite ...

If two algebraic plane curves with only ordinary singular points and cusps are related such that the coordinates of a point on either are rational functions of a ...

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 ...

The Neuberg cubic Z(X_(30)) of a triangle DeltaABC is the locus of all points P whose reflections in the sidelines BC, CA, and ABform a triangle perspective to DeltaABC. It ...

The triangle line that passes through the inner and outer Soddy centers S and S^'. The Soddy line is central line L_(657) and has trilinear equation ...

A configuration of 12 planes and 12 points such that six points lie in every plane and six planes pass through every point. Alternatively, the configuration consists of 16 ...

An ordinary double point of a plane curve is point where a curve intersects itself such that two branches of the curve have distinct tangent lines. Ordinary double points of ...

A set of four points, one of which is the orthocenter of the other three. In an orthocentric system, each point is the orthocenter of the triangle of the other three, as ...