Here are some of the handouts I've written for math training camps at the national level. As you might be able to guess, I really like geometry.
A Few (Geometry) Problems - 2021 Canada Summer Training
A few interesting problems with a different flavour from olympiad geometry.
Incircles - 2021 Canada Summer Training
Some simple facts about incircles and some not-so-simple problems about incircles.
Complete Quadrilaterals and the Miquel Point - 2021 Canada Summer Training
A closer look at a general configuration. Please let me know if you solve C7.
Projective Geometry - 2021 Canada Summer Training
Basics on projective geometry.
Ratio Chasing - 2021 Canada Winter Training
Powerful applications of Ceva's, Menelaus's, and Law of Sines. Still counts as synthetic.
Functional Equations in Number Theory - 2020 Canada Summer Training
A compilation of problems involving FEs in NT.
Polynomials in Number Theory - 2020 Canada Summer Training
A compilation of problems involving polynomials in NT.
Weird Geometry - 3020 Canada Summer Training
A grim prediction of olympiad geometry 1000 years in the future.
(Real) Functional Equations - 2020 Canada Summer Training
A compilation of problems involving FEs, mostly concerning R.
Tangent Circles - 2020 Canada Summer Training
TL;DR either use inversion or look for a Miquel point. Sometimes both.
A Few Configurations - 2020 Canada Winter Training
Around the orthocenter, incenters and excenters, and isogonal conjugates.