How are perpendiculars determined in the Kline Model?
In the Kline model, perpendiculars are determined by a new point called the pole of a chord. The pole is defined as the inverse point of a chord (Kline line) with respect to the circle. This sounds incredibly complicated, but it is actually not as confusing as it sounds. Suppose I have points A and B in my circle. I can create the chord that goes through those two points. The chord will intersect the circle at two points, and I can draw tangent lines through those intersection points. Call the intersection of the tangent lines P, which is the pole of the chord. Point P is not actually a point in the Kline disc, however we can use it to find a perpendicular. If I place a third point K in the circle and draw the line through P and K it will be perpendicular to my original chord. All I need to do now is create the chord on the line KP.
Move points A, B and K to see what happens to the construction.
What happens to P when K is moved? Why?