Search Results for "Eight Point Circle Theorem"

The Bevan point V of a triangle DeltaABC is the circumcenter of the excentral triangle DeltaJ_AJ_BJ_C. It is named in honor of Benjamin Bevan, a relatively unknown Englishman ...

The locus of the point at which two given circles possess the same circle power is a straight line perpendicular to the line joining the midpoints of the circle and is known ...

The first mid-arc point is the triangle center with triangle center function alpha_(177)=[cos(1/2B)+cos(1/2C)]sec(1/2A). It is Kimberling center X_(177).

The third Brocard point has triangle center function alpha=a^(-3) and is Kimberling center X_(76) (Kimberling 1998, p. 78). The point may have received its name since its ...

In any triangle, the locus of a point whose pedal triangle has a constant Brocard angle and is described in a given direction is a circle of the Schoute coaxal system.

The center of an inner Soddy circle. It has equivalent triangle center functions alpha = 1+(2Delta)/(a(b+c-a)) (1) alpha = sec(1/2A)cos(1/2B)cos(1/2C)+1, (2) where Delta is ...

Let the opposite sides of a convex cyclic hexagon be a, a^', b, b^', c, and c^', and let the polygon diagonals e, f, and g be so chosen that a, a^', and e have no common ...

A theorem about (or providing an equivalent definition of) compact sets, originally due to Georg Cantor. Given a decreasing sequence of bounded nonempty closed sets C_1 ...

For any point P on the boundary of an ordinary ball, find a neighborhood of P in which the intersection with the ball's boundary cuts the neighborhood into two parts, each ...

Let sigma_1, ..., sigma_4 be four planes in general position through a point P and let P_(ij) be a point on the line sigma_i·sigma_j. Let sigma_(ijk) denote the plane ...