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Looking for a textbook on 3D synthetic geometry that concerns points, lines, planes, spheres, and their intersections, tangency relations, and incidence relations. Importantly, it should NOT focus on proofs using coordinates or other analytic techniques.

A good 2D counterpart to what I am looking for would be "Euclidean Geometry in Mathematical Olympiads". Thanks in advance!

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    $\begingroup$ I don't know anything reasonably relevant that is recent (say, since the 1920s or so) or specifically designed for math competitions (and is also mostly restricted to 3D synthetic geometry), but you can find a lot of 3D synthetic geometry texts from the 1800s and early 1900s by searching with the phrase "solid geometry" in Google Books and in the Internet Archive. $\endgroup$ Commented Jul 24 at 23:37
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    $\begingroup$ Did you try volume 2 of Kiselev's "Geometry" (translated by Givental)? $\endgroup$ Commented Jul 25 at 13:40
  • $\begingroup$ Thanks, I'll look into it. $\endgroup$ Commented Jul 25 at 13:43

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