What would you suggest for me as I would like to learn how to draw geometric pictures appeared on mathematical competitions like IMO. For example, like this picture here:
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Plain Metapost has all of the tools you need to do elegant geometrical diagrams like this.
prologues := 3; outputtemplate := "%j%c.eps"; beginfig(1); % define the radius r = 100; % define four points spaced arbitrarily on a circle of radius r; z1 = (r,0) rotated 140; z2 = (r,0) rotated 72; z3 = (r,0) rotated 3; z4 = (r,0) rotated -120; % define the points on the circle half way between these points % do this by finding the angle of the vector sum of the two points z11 = (r,0) rotated angle (z1 + z2); z12 = (r,0) rotated angle (z2 + z3); z13 = (r,0) rotated angle (z3 + z4); z14 = (r,0) rotated angle (z4 + z1); % find the intersection of the lines between opposite mid points z0 = (z11--z13) intersectionpoint (z12--z14); % draw the circle in grey draw fullcircle scaled 2r withcolor .7 white; % draw some radius lines and a chord in pink drawoptions(withcolor withcolor .37 red + .5 white); forsuffixes $=11,12,13,14: draw origin -- z$; endfor draw z11 -- z14; drawoptions(); % mark the right angle draw unitsquare scaled 5 rotated angle (z12-z14) shifted z0 withcolor .7 white; % draw A-B-C-D and P-R and S-Q draw z11 -- z13; draw z12 -- z14; draw z1 -- z2 -- z3 -- z4 -- cycle; % label the points, the "scaled" trick works because everything is centred at origin s = 13/12; label("A", z1 scaled s); label("B", z2 scaled s); label("C", z3 scaled s); label("D", z4 scaled s); label("P", z11 scaled s); label("Q", z12 scaled s); label("R", z13 scaled s); label("S", z14 scaled s); label("I",z0 shifted (7,-3)); endfig; end.
This handout by Evan Chen describes two possible workflows, one using GeoGebra and one using Asymptote. There is also a thorough worked example. I've tried out the GeoGebra workflow and it worked for me, but Asymptote is even better because it integrates with TeX; however, it seems slightly more time-consuming.