Learning pack · Foundation · CIE Core

Circle Properties

What's in this pack: printable worksheet PDF, matching answers PDF (Foundation · CIE Core depth). Circle properties at foundation level focus on radius, diameter, chord language and basic angle facts before full theorem proofs.

Resources at the top · full summary · videos with short notes below.

🎒 Resources in this pack

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Scaffolded Learning Sheet — attempt the worksheet, then use the Answers for a full written solution.

📝 Open Learning Sheet ✅ Open answers 📖 Full summary

Files: foundation-23 Circle Properties handout.pdf · foundation-23 Circle Properties handout answers.pdf

Full topic summary

Circle properties at foundation level focus on radius, diameter, chord language and basic angle facts before full theorem proofs.

Key learning points

Radius is constant from centre to circumference.
Perpendicular from centre to a chord bisects the chord.
Distinguish chord, arc, sector and segment in diagrams.

Worked example 1 — Angle in a semicircle

Angle at the circumference in a semicircle?

Working

90^\circ

Angle in a semicircle is a right angle.

Worked example 2 — Chord bisector

Perpendicular from centre to a chord does what?

Working

\text{bisects the chord}

Standard circle property.

Worked example 3 — Tangent-radius

Angle between tangent and radius?

Working

90^\circ

Tangent ⊥ radius.

Worked example 4 — Tangent–radius

Tangent touches circle centre $O$ at $T$ . Angle $OT$ to the tangent?

Working

90^\circ

Radius is perpendicular to the tangent at the point of contact.

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