Let AP, BP, CP be the cevians of a point P in the plane of a triangle ABC.
Let A_{B} be a point on BP and A_{C} a point on CP such that the triangle AA_{B}A_{C} is equilateral. Define B_{C}, B_{A}, C_{A} and C_{B} cyclically.
X(5618) is the only point on the circumcircle such that the lines A_{B}A_{C}, B_{C}B_{A}, C_{B}C_{A} are concurrent.
Moreover, the centers of the three equilateral triangles are collinear with P; denote their line by L(P). If P is on the circumcircle of ABC, then L(P) passes through X(110). (Angel Montesdeoca, November 3, 2013)