Assignment Due 1/11

Inversion Constructions

1. Carry out with Sketchpad and/or straightedge and compass the constructions in Ogilvy, pp. 25-29.

2. Also, consider a construction using this figure (line OP is perpendicular to NS).  Prove that P' is the inversion of P in the circle. 

3. Tell which of the constructions in 1 and 2 are valid for all P (whether P is inside or outside the circle or on the circle and this which will make good scripts for Sketchpad).
4. In this figure, tell why the product |OC||OD| = |OE||OF| for any two circles through A and B.