Geometry Construction Tool
Construct with compass and straightedge, then drag points and watch everything follow.
Try before you buy.
- Free preview: the whole board with every tool and live measurements on a marked working view, with the SVG and PNG files and the share link locked.
- Locked until you unlock it: download and copy.
- Unlock: Pro pass, ₹179 for 30 days or ₹79 for 1 week, a one-time payment that never renews. Unlock: Pro pass, $5.99 for 30 days or $2.99 for 1 week, a one-time payment that never renews.
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Locked in the free preview. Opens the ways to unlock this result.
Locked in the free preview. Batch runs unlock with a pass.
Locked in the free preview. Query results unlock with a pass.
About the Geometry Construction Tool
A dynamic geometry board for compass-and-straightedge constructions. Place points; draw segments, lines, rays, circles and polygons; and build perpendiculars, parallels, perpendicular bisectors, angle bisectors, tangents, midpoints and intersection points from them. Reflect objects in a line, turn them half way round a point, or rotate them by any angle.
Then drag a point: everything built on it moves with it, so a construction shows what stays true for every shape, not only the one you drew. Lengths, angles and areas update live as you drag. Open a ready-made construction — Euclid’s equilateral triangle, the perpendicular bisector, a circumcircle, tangents from a point — or build your own, and keep it as a share link or an SVG or PNG picture.
How to use it
- Choose a tool in the toolbar; the line above the board says what to click next.
- Click the board to place a point, or click points, lines and circles that are already there. Clicking a line or circle makes a point that stays on it, and clicking where two of them cross makes their intersection point.
- Choose Move and drag points — or whole segments, circles and polygons — and watch everything built on them follow. Drag the empty board to pan; zoom with the mouse wheel, a pinch or the zoom buttons.
- Use the list beside the board to pick objects for a tool, hide or delete them, or move a focused point with the arrow keys (Shift for small steps). Add a point at exact coordinates with the form above the list.
- Copy a share link, or download the board as SVG or PNG — with a Pro pass or after unlocking this construction; without one you see the free preview.
Examples
Circle about A through B, circle about B through A; join A and B to a point C where they cross
|AB| = |BC| = |CA| for every position of A and B
AC and BC are radii of circles of radius AB.
Equal circles about A and B through each other; the line through their two crossings
It meets AB at its midpoint M at 90°: |AM| = |MB|
Perpendicular bisectors of AB and BC; their crossing O; the circle about O through A
The circle passes through B and C too: |OA| = |OB| = |OC|
Circle of radius 3 about O(0, 0), and P(7, 2)
Two tangents; each meets its radius at 90°, and |PT| = √(|PO|² − r²) = √44 ≈ 6.63
Triangle A(1, 1), B(4, 1), C(2, 3) reflected in the line x = −1
Both triangles have area 3; rotating the triangle 90° about the origin keeps it too
Common uses
- Practising the classical constructions — bisectors, perpendiculars, tangents, equilateral triangles — and checking them by dragging.
- Exploring a theorem: the circumcentre, the incentre, angles in a semicircle, equal tangents, and what stays true as the figure changes.
- Preparing clean diagrams of constructions for worksheets, notes and slides as SVG or PNG files.
- Showing transformations — reflections, half turns and rotations — and what they keep the same.
- Measuring lengths, angles and areas of a figure without a ruler or protractor.
Constructions with compass and straightedge
The classical constructions use only a straightedge (to draw the line through two points) and a compass (to draw a circle about a centre). The board’s Line, Segment, Ray, Circle and Compass tools are those two instruments; Intersect marks where the lines and circles cross. With them you can follow Euclid step by step: an equilateral triangle on a segment (I.1), bisecting an angle (I.9), bisecting a segment (I.10) and a tangent from a point to a circle (III.17). The shortcut tools — Perpendicular, Parallel, Perpendicular bisector, Angle bisector, Midpoint and Tangents — give the same objects in one step once the construction is understood.
Movable and dependent objects
A point you place on the empty board is movable: it can be dragged anywhere. A point on a line or circle can be dragged along it. Every other object is dependent: an intersection, a midpoint, a perpendicular or a reflected copy is worked out again from the objects it was built from each time one of them moves. When a construction becomes impossible in a position — two circles that no longer meet, a tangent from a point inside the circle — the objects that depend on it are left out, and the list says they are not defined there; they come back as soon as the position allows. Of the two points where a line meets a circle, or where two circles meet, each intersection point keeps to its own side as you drag.
Measurements and transformations
- Length of a segment or the distance between two points: √((x₂ − x₁)² + (y₂ − y₁)²).
- Angle ABC at the vertex B, between the rays BA and BC, from 0° to 180°; a right angle is marked with a small square.
- Area of a polygon by the shoelace formula ½|Σ(xᵢyᵢ₊₁ − xᵢ₊₁yᵢ)|, or of a circle, πr²; the list also gives each polygon’s perimeter and each circle’s radius.
- Reflect in a line mirrors an object; reflect through a point turns it half way round that point; rotate turns it anticlockwise about a centre by the angle you type. The images move with the original.
Values are rounded to the decimal places you choose (0 to 4).
Sharing and saving
The share link holds the whole construction in the part of the address after “#”, which browsers keep to themselves and never send to a server; opening the link rebuilds the board exactly. The SVG file is a drawing that stays sharp at any size and opens in browsers and drawing programs; the PNG file is a picture at twice the board’s size. The board is not stored in your browser: keep a link or a file to come back to a construction.
Limitations
- Up to 400 objects on a board; coordinates within ±1,000,000.
- Plane Euclidean geometry only: no loci, curves through five points, text boxes or three-dimensional figures.
- The board is not saved in the browser: keep the share link or a file to return to a construction.
- Measurements are worked out in floating point and rounded to at most 4 decimal places.
- Exact positions by keyboard come from the coordinate form and the arrow keys; snapping to the grid helps with the mouse.
Privacy
On this device: nothing is sent
Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot.
Frequently asked questions
What do I get without a pass?
Without a pass, Geometry Construction Tool shows the whole board with every tool and live measurements on a marked working view, with the SVG and PNG files and the share link locked. Until you unlock it, the result can’t be downloaded or copied. A Pro, Premium or Ultimate pass, a one-time payment that never renews, unlocks the full result. The pricing page lists the passes and their prices.
How do I construct the perpendicular bisector of a segment with a compass?
Draw a circle about A through B and a circle about B through A. They cross at two points; the line through those points is the perpendicular bisector, and it meets AB at its midpoint. On the board: Circle (A, then B), Circle (B, then A), Intersect (the two circles), then Line through the two new points. The Perpendicular bisector tool does the same in one step.
How do I bisect an angle?
Choose Angle bisector and click a point on one arm, then the vertex, then a point on the other arm. With compass and straightedge: draw a circle about the vertex, mark where it crosses the two arms, draw equal circles about those two points, and join the vertex to where those circles meet. Measure the two halves with the Angle tool to check.
Why did part of my construction disappear when I moved a point?
In that position it cannot be constructed: for example the two circles no longer meet, so their intersection point does not exist, and everything built on it goes with it. Move the point back and it returns. The list of objects marks such objects as not defined in this position.
Can I place points at exact coordinates?
Yes. Type x and y in Add a point by its coordinates (fractions such as −1/2 work). You can also switch on snapping to the grid, or focus a point in the list and move it with the arrow keys, one grid step at a time or a tenth of a step with Shift.
What is the difference between a movable point and a dependent point?
A movable point is placed by you and can be dragged anywhere; a dependent point, such as an intersection or a midpoint, is worked out from other objects and moves only when they move. Dragging a movable point is how you test a construction: if the property you built holds in every position, the construction is right.
How do I share a construction?
Copy the share link: it holds the whole construction in the address after “#”, so whoever opens it gets the same board, ready to drag. The SVG and PNG downloads give a picture for documents and slides.