Geometric Construction
Geometric Construction
This domain tests compass-and-straightedge constructions: bisectors, perpendiculars, angles, regular polygons, tangents and loci. Marks are for accurate arcs and a clean final figure, not for measured guesses.
Core rules
- A perpendicular bisector is the locus of points equidistant from two endpoints; an angle bisector is the locus equidistant from two sides.
- Construct 60° by stepping the compass radius along an arc; obtain 30°, 15°, 45° and 75° by bisecting or combining constructed angles.
- In a regular polygon, vertices divide the circumcircle into equal arcs. For a hexagon the chord equals the radius; a square uses perpendicular diameters.
- A tangent touches a circle at one point and is perpendicular to the radius at that point. From an external point, the two tangent lengths are equal.
Worked example
Construct a regular hexagon in a 30 mm-radius circle. Draw the circle and a horizontal diameter AB. Keep the compass at 30 mm. With centre A, cut the circle at C and F; with centre B, cut it at D and E. Join A-C-D-B-E-F-A. Reasoning: each step marks a 60° arc, so every chord equals the radius; six equal chords close exactly at A.
Traps that cost marks
- Setting the compass by ruler measurement instead of transferring the radius.
- Erasing construction arcs that prove the method.
- Drawing a tangent through the contact point without showing the perpendicular radius.
- Letting polygon vertices drift off the circumcircle.