Help on Ex. 55

Hello there!

I am from the Czech Republic and thus my Math education was nearly completely proof-less. Thus I have started reading How to Prove It by Velleman for general proofs and Kiselev's Geometry to brush up my planimetry / stereometry (which I lack intention for and generally I'm pretty bad at, even tough the rest of high school math is easy for me and I'm want to study Math at a university) and to learn how to do geometrical proofs.

I'm stuck on exercise 55. I have tried to work with the definitions from the preceding chapter but to no avail. It maybe because I have nearly zero experience with geometrical proofs, so any tips and tricks would be highly appreciated.

So far I have tried to proof this by cases (ie. convex / non convex, complex / non complex), but I don't know how to continue.

I feel really ashamed as this is Grade 7 material that I cannot do in the last year of high school.