to pit two others against each other in order to achieve a desired outcome or to gain an advantage; to "play both ends against the middle"
It is one thing to triangulate between the United States and the Arab world for short-term advantage; quite another to find oneself alienated from the heretofore supportive Americans without finding commensurate gratitude from the Middle East.
survey by triangulation; "The land surveyor worked by triangulating the plot" measure by using trigonometry; "triangulate the angle" divide into triangles or give a triangular form to; "triangulate the piece of cardboard" composed of or marked with triangles