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The intersection Fl of the Gergonne line and the Soddy line. In the above figure, D^', E^', and F^' are the Nobbs points, I is the incenter, Ge is the Gergonne point, and S ...

According to G. Pólya, the method of finding geometric objects by intersection. 1. For example, the centers of all circles tangent to a straight line s at a given point P lie ...

The perpendicular foot, also called the foot of an altitude, is the point on the leg opposite a given vertex of a triangle at which the perpendicular passing through that ...

Let the center B of a circle of radius a move along a line BA. Let O be a fixed point located a distance c away from AB. Draw a secant line through O and D, the midpoint of ...

Let DeltaH_AH_BH_C be the orthic triangle of a triangle DeltaABC. Then each side of each triangle meets the three sides of the other triangle, and the points of intersection ...

Coaxal circles are circles whose centers are collinear and that share a common radical line. The collection of all coaxal circles is called a pencil of coaxal circles ...

Given a curve C and O=(x_0,y_0) a fixed point called the pedal point, then for a point P on C, draw a line perpendicular to OP. The envelope of these lines as P describes the ...

Two planes always intersect in a line as long as they are not parallel. Let the planes be specified in Hessian normal form, then the line of intersection must be ...

A horizontal line placed above multiple quantities to indicate that they form a unit. It is most commonly used to denote 1. A radical (sqrt(12345)), 2. Repeating decimals ...

If three circles A, B, and C are taken in pairs, the external similarity points of the three pairs lie on a straight line. Similarly, the external similarity point of one ...