Olympiad geometry diagrams, drawn from the problem statement

Last updated 28 October 2026

Olympiad geometry problems are where a hand-drawn sketch fails first: tangent circles that must touch exactly, a second intersection that must be the right one, an arc that must not contain a vertex, a point that lies inside the triangle only in one configuration. makegeodiagrams.com draws such a problem from its statement: the conditions become a construction, the construction is solved so that every one of them holds, the claim is checked on the figure, and the figure is printed by Asymptote the way a contest booklet or a solutions book prints it. The gallery shows figures of IMO problems from 2003 to 2022, IMO shortlist problems and Sharygin olympiad problems, each of them live.

What an olympiad figure has to get right

• Named objects of the triangle and the circle. Incircle and excircles, circumcircle and nine-point circle, the orthocentre, centroid, incentre and excentres, the Euler line, symmedians and the symmedian point, mixtilinear incircles, the Miquel point, arc midpoints, antipodes, the Humpty, Dumpty, Queue and Sharky-Devil points and many more are built as themselves, never approximated.
• Tangency. A circle tangent to a line or to another circle touches it exactly, internally or externally as the statement says; a line stated tangent to a circle reaches its touch point; circles inscribed in an angle sit in that angle.
• The right intersection. "The line AD meets the circumcircle again at X" picks the second intersection; "the arc BC not containing A" is that arc; "P inside the triangle" and "on the extension of AB beyond B" are kept as stated.
• The claim is checked, and drawn apart. The conclusion is tested numerically on the drawn figure and reported as holding or failing; what holds is drawn dashed in its own colour, so a conclusion never reads as a given. Equal segments, equal angles and right angles are marked only where the statement states them.
• A generic figure. The figure shown is a general position of the problem, never the isosceles or symmetric special case the statement did not ask for; a figure in which points coincide or a triangle collapses is refused. "Draw another figure" gives a genuinely different layout.
• Loci and invariants. A locus problem comes back with the locus traced on the figure and named; a point that stays fixed as something moves is shown fixed, and the live figure lets you move the given points and watch.

Examples from the gallery

Each of these was drawn from the statement in the ordinary chat; drag any point on its page and the whole construction follows.

• IMO 2008 Problem 6: a circle tangent to the lines of a quadrilateral, with tangency points reached by the lines that touch the circle.
• IMO 2015 Problem 3: tangent circumcircles in an acute triangle.
• IMO 2019 Problem 6: the incircle, its touch points and a perpendicular through one of them.
• IMO Shortlist 2021 G4: a cyclic quadrilateral and the tangent at D.
• Sharygin 2008, correspondence round, problem 13: excircle touch points and a point on the incircle.
• Sharygin 2005, final round, grade 10, problem 6: a circle on a diameter and three concurrent lines.

Where the figures go

• A solution write-up or a handout in LaTeX: the PDF or SVG with \includegraphics, or the Asymptote source itself, which compiles to the same figure with labels in Computer Modern.
• A forum post: the Asymptote code pasted as it is, or a PNG at 300 or 600 dpi.
• A problem booklet or a book: the printed size is chosen per figure, from about 7 cm for a plain triangle to 16 cm for a crowded configuration, the way olympiad booklets size theirs, and you can set it yourself.
• A web page or an online book: a live figure whose points the reader drags, exported as a small self-contained page.
• A solution's own figure: attach the solution and get the figure that belongs next to it, with the points, lines and circles the proof introduces.

How to use it for a contest problem

1. Paste the complete statement exactly as written, in plain text or LaTeX; the notation is read in any spelling and the chat shows it typeset.
2. Read the reply: it lists every condition and claim that was checked. A claim that fails is reported, not drawn; a statement that cannot be drawn says so instead of showing a different problem.
3. Restyle with Effects (grayscale for print, focus on the stated objects, cropped big circles), change anything in the design editor or by asking in words, and download SVG, PDF, PNG or the Asymptote source.

More answers are on the questions page; the plans and what each includes are on the plans page.