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The contact triangle of a triangle DeltaABC, also called the intouch triangle, is the triangle DeltaC_AC_BC_C formed by the points of tangency of the incircle of DeltaABC ...

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 fast boat is overtaking a slower one when fog suddenly sets in. At this point, the boat being pursued changes course, but not speed, and proceeds straight in a new ...

Abstractly, a spatial configuration F is said to possess rotational symmetry if F remains invariant under the group C=C(F). Here, C(F) denotes the group of rotations of F and ...

Gaussian curvature, sometimes also called total curvature (Kreyszig 1991, p. 131), is an intrinsic property of a space independent of the coordinate system used to describe ...

Draw lines P_AQ_A, P_BQ_B, and P_CQ_C through the symmedian point K and parallel to the sides of the triangle DeltaABC. The points where the parallel lines intersect the ...

A curve which has at least multiplicity r_i-1 at each point where a given curve (having only ordinary singular points and cusps) has a multiplicity r_i is called the adjoint ...

The point of concurrence of the four maltitudes of a cyclic quadrilateral. Let M_(AC) and M_(BD) be the midpoints of the diagonals of a cyclic quadrilateral ABCD, and let P ...

Suppose P=p:q:r and U=u:v:w are points, neither lying on a sideline of DeltaABC. Then the P-anticomplementary conjugate of U is the point where h(a,b,c,p,q,r,u,v,w) ...

Barycentric coordinates (t_1,t_2,t_3) normalized so that they become the areas of the triangles PA_1A_2, PA_1A_3, and PA_2A_3, where P is the point whose coordinates have ...