How much have you learned in classical plane geometry? Have you done things like Menelaus and Ceva theorem? There are a lot of pretty stuffs in geometry that are not covered in high school syllabus, but they appear frequently in mathematical olympiads.
You may want to read, if you have not already, Coxeter's book "Geometry Revisited
If you know, or don't mind to learn, some complex numbers, you can do many interesting geometry problems using complex numbers. I recommend "Complex Numbers and Geometry"