The center bisects all chords through it (§ 39).
Every diameter passes through the center.
All chords through the same point at infinity (that is, each of a set of parallel chords) are bisected by the diameter which is the polar of that infinitely distant point.
109. Conjugate diameters. We have already defined conjugate lines as lines which pass each through the pole of the other (§ 100).
Any diameter bisects all chords parallel to its conjugate.
The tangents at the extremities of any diameter are parallel, and parallel to the conjugate diameter.
Diameters parallel to the sides of a circumscribed parallelogram are conjugate.
All these theorems are easy exercises for the student.