Exercise 3.6 (explanation)
- Author:
- Gianluca Occhetta
Let F be the intersection of the line AC with the perpendicular line through O.
The triangles ADB and APO are similar (by SIM AAA), hence AO/AB=OP/BD.
The triangles ABC and AOF are similar (by SIM AAA), hence AO/AB=OF/BC.
Since BD=BC we have OP=OF.
A similar construction shows that OG=OP, where G is the intersection of the other line with the perpendicular line through O.