In The Almagest, we found the original Ptolemy’s theorem and its proof, and we compared it to “Ptolemy’s theorem” written in two modern geometry textbooks. They are different in that the new ones include the “converse” of the original one. We noticed the hypothesis of the “converse” can be interpreted in two ways. Using this as our motivation, we establish a new theorem related to Ptolemy’s theorem in this note as follows: If four distinct points A, B, C, D are given in the three-dimensional space so that ABC is a triangle, and if \(|AB||CD|+|AD||BC|=|AC||BD|,\) then the points A, B, C, D are not only on the same plane, but ABCD is also a cyclic quadrilateral.