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Let the inner and outer Soddy triangles of a reference triangle DeltaABC be denoted DeltaPQR and DeltaP^'Q^'R^', respectively. Similarly, let the tangential triangles of ...

Given a point P in the interior of a triangle DeltaA_1A_2A_3, draw the cevians through P from each polygon vertex which meet the opposite sides at P_1, P_2, and P_3. Now, ...

Given a triangle DeltaABC, construct the contact triangle DeltaDEF. Then the Nobbs points are the intersections of the corresponding sides of triangles DeltaABC and DeltaDEF, ...

There are (at least) three different types of points known as Steiner points. The point S of concurrence of the three lines drawn through the vertices of a triangle parallel ...

The 60 Pascal lines of a hexagon inscribed in a conic intersect three at a time through 20 Steiner points, and also three at a time in 60 points known as Kirkman points. Each ...

"The" Griffiths point Gr is the fixed point in Griffiths' theorem. Given four points on a circle and a line through the center of the circle, the four corresponding Griffiths ...

The point on a line segment dividing it into two segments of equal length. The midpoint of a line segment is easy to locate by first constructing a lens using circular arcs, ...

The first Napoleon point N is the concurrence of lines drawn between vertices of a given triangle DeltaABC and the opposite vertices of the corresponding inner Napoleon ...

Let points A^', B^', and C^' be marked off some fixed distance x along each of the sides BC, CA, and AB. Then the lines AA^', BB^', and CC^' concur in a point U known as the ...

Points, also called polar reciprocals, which are transformed into each other through inversion about a given inversion circle C (or inversion sphere). The points P and P^' ...