Exercise 37.2
- Author:
- Gianluca Occhetta
Prove that the following construction with compass alone gives the inverse
of A in Г (provided that OA > r/2):
Draw a circle with center A through О to meet Г at Ρ and Q. Then draw
circles with centers Ρ and Q through О to meet at A' (3 steps).
The isosceles triangles AOP and POC are similar, since they share the angle in O. It follows that AO/OP = OP/OA', so OA*OA' = r^2