Geometric Constructions Calculator
Step-by-step ruler-and-compass constructions with a scale drawing: triangles from SSS, SAS, ASA and RHS, dividing a segment in a ratio, and tangents from an outside point, with the measurements to check your drawing.
About the Geometric Constructions Calculator
A construction uses only a ruler (to draw lines) and compasses (to draw arcs and copy lengths), plus a protractor where the syllabus allows. Each step here is one action you can do on paper, and the drawing shows the finished figure to scale.
The other sides and angles are calculated so you can check your figure with a ruler and protractor.
The formula
AP : PB = m : n; tangent length = √(OP² − r²)
Worked example
Example: Triangle ABC = ∠A ≈ 78.463°, ∠B ≈ 57.1217°, ∠C ≈ 44.4153°
- Inputs: Construct: A triangle from three sides (SSS); BC (base): 7; CA: 6; AB: 5.
- Formula: AP : PB = m : n; tangent length = √(OP² − r²)
- Draw BC = 7 cm.
- With centre B and radius 5 cm (AB), draw an arc.
- With centre C and radius 6 cm (CA), draw an arc cutting the first at A.
- Join AB and AC.
- Check by measuring the parts you didn't use. AB ≈ 5, CA ≈ 6, ∠A ≈ 78.463°, ∠B ≈ 57.1217°, ∠C ≈ 44.4153°
- Result: Triangle ABC = ∠A ≈ 78.463°, ∠B ≈ 57.1217°, ∠C ≈ 44.4153°
- Sides (BC, CA, AB): 7, 6, 5 cm
- Angles (A, B, C): 78.463°, 57.1217°, 44.4153°
Questions people ask
Why does dividing a segment this way work?
The parallel line cuts the two sides of triangle ABA₍ₘ₊ₙ₎ in the same ratio (basic proportionality theorem).
Can I construct any angle with compasses?
Angles built from 60° and 90° by bisecting and adding (30°, 45°, 75°, 105°, 120°…) can; others need a protractor.