I used to think a lot about plane geometry when I was in high school. There are many beautiful results and many of the times, proving them are actually quite tricky.

I published a few papers about this area back then.

Publications

1. A Synthetic Proof of Goormaghtigh's Generalization of Musselman's Theorem, Forum Geometricorum, 5 (2005) 17-20 (pdf).

2. On the Complement of the Schiffler Point, Forum Geometricorum, 5 (2005) 149-164 (pdf).

3. (with Salazar, J.C.) On mixtilinear incircles and excircles, Forum Geometricorum, 6 (2006) 1- 16 (pdf).

4. A note on the barycentric square roots of Kiepert perspectors, Forum Geometricorum, 6 (2006) 263-268 (pdf).

5. (with Andrica, D.) A note on Nagel and Gergonne points, Creative Mathematics and Informatics, 17 (2008) 127-136 (pdf).

Darij Grinberg and I also proved a very nice and tricky problem about the Schroeder point. See it here.

Some other problems that I proposed can be found here(pdf).

There was also a paper I wrote sometime in high school about trigonometry where I gave very short proofs to Garfulkel’s inequalities. The trick is quite neat and I like it very much. It can help solve some very tricky inequality problems.