hyperbolic and elliptic involution

Ben Geels
Given a circle and three horizontal lines a, d and f line a cuts the circle in J and K d and f do not cut the circle A point A is given on line a. The polar line of A cuts line a in B. The points A and B are in hyperbolic involution wrt J and K Likewise points C and D, now the involution is elliptic. The same counts for points E and F