Ptolemy's Theorem in Equilateral Triangle

Quadrilateral $XYPZ$ is cyclic. By Ptolemy's Theorem on cyclic quadrilateral $XYPZ$: $XP \cdot YZ = YP \cdot XZ + PZ \cdot XY$. Since $\triangle XYZ$ is equilateral, $XY = YZ = XZ = s$. $XP \cdot s = YP \cdot s + PZ \cdot s \implies XP = YP + PZ$.