Verified diagrams for olympiad geometry

Paste a geometry problem.
Get a figure that is actually correct.

COMPAS translates an olympiad-style statement into a constructive program, solves the construction numerically, and only then draws it. Every diagram you see compiled, solved and passed its own checks — then you refine it in plain English.

Open the chat → See how it works

Sign-in required · your past conversations are saved and searchable.

IMO 2000 · Problem 1 · verified

“Two circles meet at M and N. AB is tangent to both; CD is parallel to AB through M. Lines AC and BD meet at E; AN and BN meet CD at P and Q. Show that EP = EQ.”

IMO 2000 Problem 1: two intersecting circles with a common tangent, the parallel chord through M, and E equidistant from P and Q

How a conversation works

One chat per problem. The first message builds the figure; every message after it edits the same figure — and each answer is a new version you can step back to.

State the problem

Paste the statement, LaTeX and all. It is translated into an EGML construction program, then compiled and solved — failures are fed back and repaired automatically.

Read a verified drawing

The figure is rendered through Asymptote, the same pipeline that produces the project's PDFs. Marks, labels and dashed helper lines follow the statement — never the coordinates.

Refine in plain English

“Draw the circumcircle dashed”, “remove AF”, “make BC the bottom side”. Additions go through the verified program; edits to existing ink are applied to the drawing, so the layout stays put.

Figures from real conversations

Each of these came out of a single chat turn — statement in, solved construction out.

Triangle with its incircle and touch point

Incircle touch point The incircle touches BC at D; M is the midpoint of BC.

Obtuse triangle inscribed in its circumcircle

Circumcircle Γ An obtuse triangle, its circumcircle and a tangent construction.

Triangle with circumcenter and orthocenter

Circumcenter and orthocenter Altitudes drawn because the construction states them.

Browse the full gallery — 171 figures →

What you get

The chat is a thin layer over the construction engine — everything it draws has been checked.

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Verified, not sketched

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

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Draw another figure

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

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Versions, never overwritten

Every turn appends a version. Reopen an earlier one and edit from there — branching is just clicking back.

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Searchable history

Past conversations are saved on the server and searchable from the sidebar, with all of their figures.

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Asymptote quality

The figure shown is the Asymptote rendering, downloadable as SVG, with its source one click away.

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Honest edits

If an instruction changes nothing, the reply says so instead of quietly shipping the same drawing again.

Paste a geometry problem.Get a figure that is actually correct.