What it does
This is a small dynamic geometry sketchpad, the kind used to explore school and university geometry. You place points and build on them: segments, lines, circles, midpoints, perpendiculars, parallels, perpendicular bisectors, angle bisectors and intersections. Every object remembers how it was made, so when you drag a point, everything built on it moves too and every measurement updates. That is how you see that a property holds for every triangle, not just the one you drew.
How to use it
- Pick a tool. The line under the tools says what to tap next.
- Tap on the drawing. Where a tool needs a point, tap an existing point or an empty spot (which makes a new point there). Where it needs a line or circle, tap on it.
- Drag any free point (a filled dot) to move it, in any tool. Points made by a construction, such as midpoints and crossings, are hollow and move only when what they depend on moves.
- The Objects and measurements table lists everything with its value: points as coordinates, lines as equations y = mx + c, circles with centre, radius and area, polygons with area and perimeter. Type new coordinates for a free point to place it exactly. The × removes an object and everything built on it. Undo steps back.
Tools
- Segment, Line (infinite), Circle (centre, then a point on it), Midpoint.
- Perpendicular and Parallel: tap a line or segment and a point, in either order.
- Perpendicular bisector of two points, and Angle bisector (a point on one arm, the corner, a point on the other arm).
- Intersect: tap two lines or circles. A line and a circle, or two circles, can cross twice, so both crossings are made; one that does not exist at the moment is listed as “does not exist now” and appears when the shapes meet.
- Distance, Angle (0° to 180°) and Polygon (tap the corners, then the first corner again) for measurements.
Grid shows the coordinate grid. Snap to the grid puts new and dragged points on the nearest half unit.
Worked example
The opening example draws the triangle A (−4, −2), B (3, −3), C (1, 4), the perpendicular bisectors of AB and BC, and their crossing D, the circumcentre, at (−0.159574, −0.117021). The circle centred at D through A has radius 4.2772, and the three distances d1 = DA, d2 = DB and d3 = DC are all 4.2772: drag any corner and they stay equal. The angle ABC is 65.9245°.
The “Incircle” example uses two angle bisectors to find the incentre D (0.0623325, −0.438), drops a perpendicular to AB to find where the incircle touches it, and shows the inradius 2.1208, which equals the area 23.5 divided by half the perimeter. “Midpoints of a quadrilateral” shows Varignon’s theorem: joining the midpoints of any quadrilateral’s sides gives a parallelogram with exactly half the area (63 and 31.5 in the example).
Good to know
Angles are measured between 0° and 180°. Points cannot yet be tied to lie on a line or circle, and there are no locus or transformation tools. Lengths are in grid units.
Frequently asked questions
Is my work saved? No. Nothing is stored or sent anywhere; download an SVG or CSV to keep it.
Can I use it on a phone? Yes. Tap to place and drag with one finger. The drawing does not scroll the page, so scroll beside it.
Where the numbers come from
- Standard coordinate geometry (line and circle intersections, shoelace area); no outside data.
- Checked against Python sympy: circumcentre, circumradius, incentre, area, angle and perimeter of a triangle, line–circle and circle–circle intersections, and the foot of a perpendicular.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.