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Paste a Euclidean geometry problem.
Get a publication-quality diagram
that’s actually correct.

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IMO 2000 · Problem 1 ↓ SVG
You paste

Circles G1 and G2 meet at M and N. A common tangent touches G1 at A and G2 at B, with M closer to line AB than N is. The line through M parallel to AB meets G1 again at C and G2 again at D. Lines AC and BD meet at E, and lines AN and BN meet CD at P and Q, respectively. Prove that EP = EQ.

You get Generated automatically · no hand edits
Compiled & solved EP = EQ verified Drawn by Asymptote

Tested on geometry problems from

IMOUSAMOSharygin Olympiad

One chat per problem. The first message builds the figure; every message after it edits the same one.

1

State the problem

Paste the statement, LaTeX and all. It becomes a construction program that is compiled and solved; failures are repaired automatically.

2

Read a verified figure

Rendered through Asymptote. Marks, labels and helper lines follow the statement — never the coordinates.

3

Refine it

Ask in plain English, or open the design editor. Each answer is a new version you can step back to.

Everything it draws has been checked.

A quiet chat over a construction engine, so the figure is right before it is pretty.

Verified, not sketched

Compile, least-squares solve, check. A figure that cannot be solved is never shown as if it were.

Translated to a construction programEGML
Compilednames · types · arity
Solvedleast squares
Goals checkedon the solved figure
RenderedAsymptote

Edit the design by hand

Restyle, rotate, move labels, add constructions. No model call, no cost.

SelectPointSegmentLineRayCircle (3 pts) MidpointIntersectPerpendicularAngle bisectorRight angle
Colour Width

Refine in plain English

Additions go through the verified program. If a request changes nothing, the reply says so.

draw the circumcircle of ABC dashed Added the circumcircle of ABC, dashed. make BC dashed BC is already dashed — nothing changed, so no new version.

Draw another figure

Re-solve the same construction from fresh seeds and keep the layout that scores best on the diagram-quality metric.

seed 1
kept · best layout
seed 3

Versions and history

Every turn appends a version you can branch from. Past conversations stay searchable, figures included.

incircle v1v2v3
Triangle with its incircle and excircle…the incircle touches BC at D and the excircle at E…
Tangential quadrilateral ABCD…with incircle ω centred at I…
Mixtilinear touch point…the A-mixtilinear incircle touches the circumcircle at T…

Publication-quality output

The figure is the Asymptote rendering itself, downloadable as SVG, PDF or PNG, with its source one click away.

figure.asy↓ Download SVG
size(13cm);
draw(A--B--C--cycle, linepen);
draw(circle(O, abs(A-O)), circlepen);
draw(A--H, dashed);
dot("$H$", H, S);

Ready when you are.

Bring a problem statement. Most figures take seconds; the hardest problems, a few minutes.

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