Search Results for ""

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, ...

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 ...

Any triangle that has two equal angle bisectors (each measured from a polygon vertex to the opposite sides) is an isosceles triangle. This theorem is also called the ...

The midpoint of the first and second Brocard points Omega and Omega^'. It has equivalent triangle center functions alpha = a(b^2+c^2) (1) alpha = sin(A+omega), (2) where ...

Given any triangle ABC, the signed sum of perpendicular distances from the circumcenter O to the sides (i.e., signed lengths of the pedal lines from O) is OO_A+OO_B+OO_C=R+r, ...

A circumellipse is a circumconic of a triangle that is an ellipse. There is an amazing formula for the area of a circumellipse. Let d_A be the length of the chord of the ...

The first Fermat point X (or F_1) (sometimes simply called "the Fermat point," Torricelli point, or first isogonic center) is the point X which minimizes the sum of distances ...

The Fuhrmann center Fu is the center of the Fuhrmann circle, given by the midpoint of the line joining the Nagel point and orthocenter (which forms a diameter of the Fuhrmann ...

A conic section that is tangent to all sides of a triangle is called an inconic. Any trilinear equation of the form ...

If the vertices A, B, and C of triangle DeltaABC lie on sides QR, RP, and PQ of the triangle DeltaPQR, then the three circumcircles CBP, ACQ, and BAR have a common point X. ...