There are books about counterexamples in analysis, topology or probability. Is there any book that focuses on counterexamples in plane geometry or loopholes in geometrical proofs?
I am particularly interested in books that illustrate "honest" false proofs of high-school geometry statements, something like Lewis Carroll's proof that every obtuse angle is equal to a right angle. I vaguely remember that there was a geometry book that discussed, in a small section, how some geometrical proofs contain loopholes because the proof writers forget about the concept of betweenness, but I can't recall the title.
Edit. After browsing on amazon.com for hours, I found a book that might be relevant:
According to an MAA review, this is actually a compilation of two separate books, Proof in Geometry by Fetisov and Mistakes in Geometric Proofs by Dubnov. The review is only neutral, and I have yet to see if the proofs are good (or should I say "bad"?) enough.