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Let a chord of constant length be slid around a smooth, closed, convex curve C, and choose a point on the chord which divides it into segments of lengths p and q. This point ...

The inner Napoleon circle, a term coined here for the first time, is the circumcircle of the inner Napoleon triangle. It has center at the triangle centroid G (and is thus ...

A right triangle with the two legs (and their corresponding angles) equal. An isosceles right triangle therefore has angles of 45 degrees, 45 degrees, and 90 degrees. For an ...

The lines joining the vertices A, B, and C of a given triangle DeltaABC with the circumcenters of the triangles DeltaBCO, DeltaCAO, and DeltaABO (where O is the circumcenter ...

In elementary geometry, orthogonal is the same as perpendicular. Two lines or curves are orthogonal if they are perpendicular at their point of intersection. Two vectors v ...

The outer Napoleon circle, a term coined here for the first time, is the circumcircle of the outer Napoleon triangle. It has center at the triangle centroid G (and is thus ...

The 60 Pascal lines of a hexagon inscribed in a conic section intersect three at a time through 20 Steiner points. There is a dual relationship between the 15 Plücker lines ...

Given an obtuse triangle, the polar circle has center at the orthocenter H. Call H_i the feet. Then the square of the radius r is given by r^2 = HA^_·HH_A^_ (1) = HB^_·HH_B^_ ...

The chord through a focus parallel to the conic section directrix of a conic section is called the latus rectum, and half this length is called the semilatus rectum (Coxeter ...

If three conics pass through two given points Q and Q^', then the lines joining the other two intersections of each pair of conics P_(ij)P_(ij)^' are concurrent at a point X ...