Plane Geometry: Circles and Constructions — CSEC Technical Drawing
This topic covers the parts of a circle and the geometric constructions associated with circles, tangents and loci.
Parts of a circle
- Centre — the middle point.
- Radius — distance from the centre to the circumference.
- Diameter — a line through the centre joining two points on the circumference (twice the radius).
- Circumference — the distance around the circle (πd).
- Chord — a straight line joining two points on the circumference (not through the centre).
- Arc — part of the circumference.
- Sector — a "slice" bounded by two radii and an arc.
- Segment — the area between a chord and an arc.
- Tangent — a line that touches the circle at exactly one point and is perpendicular to the radius at that point.
Key constructions
You should be able to:
- Find the centre of a given circle or arc (by bisecting two chords).
- Construct a tangent to a circle from a point on it or outside it.
- Draw circles to touch lines or other circles (internal and external contact).
- Divide a circle into equal parts to construct inscribed polygons.
Loci
A locus is the path traced by a point moving according to a rule — for example, points a fixed distance from a centre form a circle, and points equidistant from two lines lie on the angle bisector.
Exam tips
- Learn all the parts of a circle precisely (chord vs diameter; sector vs segment).
- A tangent is perpendicular to the radius at the point of contact.
- Find a circle's centre by bisecting two chords — they meet at the centre.
- Show light construction lines and leave them visible in geometry questions.