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If the three straight lines joining the corresponding vertices of two triangles ABC and A^'B^'C^' all meet in a point (the perspector), then the three intersections of pairs ...

Consider Kimberling centers X_(20) (de Longchamps point Z; intersection L_S intersection L_E of the Soddy line and Euler line), X_(468) (intersection L_E intersection L_O of ...

Given a succession of nonsingular points which are on a nonhyperelliptic curve of curve genus p, but are not a group of the canonical series, the number of groups of the ...

Let a, b, and c be the side lengths of a reference triangle DeltaABC. Now let A_b be a point on the extension of the segment CA beyond A such that AA_b=a. Similarly, define ...

Let A be a closed convex subset of a Banach space and assume there exists a continuous map T sending A to a countably compact subset T(A) of A. Then T has fixed points.

The Moses circle is defined as the circle with center at the Brocard midpoint X_(39) that is tangent to the nine-point circle at the center of the Kiepert hyperbola X_(115). ...

Every bounded infinite set in R^n has an accumulation point. For n=1, an infinite subset of a closed bounded set S has an accumulation point in S. For instance, given a ...

The Bevan circle, sometimes also called the excentral circle, is the circumcircle of the excentral triangle of the reference triangle, i.e., it is the circle passing through ...

If the tangents at B and C to the circumcircle of a triangle DeltaABC intersect in a point K_1, then the circle with center K_1 and which passes through B and C is called the ...

The Brocard circle, also known as the seven-point circle, is the circle having the line segment connecting the circumcenter O and symmedian point K of a triangle DeltaABC as ...