Circle parts and basic properties
Mastering circle vocabulary is non-negotiable: every G9/G10 question opens with a labelled diagram and assumes correct names.
Vocabulary
- Centre — fixed point O.
- Radius — line from O to any point on the circle. Length r.
- Diameter — chord through O. Length 2r.
- Chord — straight line joining any two points on the circle.
- Arc — part of the circle (curved). Major arc = longer; minor arc = shorter.
- Sector — region bounded by two radii and an arc. Like a pizza slice.
- Segment — region bounded by a chord and an arc. Major / minor segment depending on which side of the chord.
- Tangent — straight line touching the circle at exactly one point. The tangent is perpendicular to the radius at the point of contact.
Key formulae
- Circumference = πd = 2πr
- Area = πr²
- Arc length = (θ / 360) × πd = (θ / 360) × 2πr
- Sector area = (θ / 360) × πr²
θ is the angle at the centre, in degrees.
Tangent property (basic)
The radius OT to the tangent point T is perpendicular to the tangent line. So in any triangle formed by a tangent + radius + line to centre, you have a right angle at T. Use Pythagoras to find unknown lengths.
Two tangents from an external point
Two tangents drawn from the same external point P to the same circle have equal length. The line OP bisects the angle between the two tangents and bisects the chord joining the two tangent points perpendicularly.
WJEC exam tip
Always label your diagram before computing. Mark right angles where the tangent meets a radius. Quote the tangent–radius perpendicularity as a reason — WJEC awards a B1 communication mark in many tangent questions for stating it explicitly.
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