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HomeQuestion 1FluencyCore
Original practice · Free Online RevisionSkill · centre-circumference theorem
An angle at the centre subtending arc AB is 118°. Find the angle at the circumference subtending the same arc.
Geometry & MensurationAdvancedMaths revision
Circle Theorems (Advanced)
Use circle theorems in multi-step proofs and angle calculations.
Focus points
✓Use central and circumferential angle theorems.
✓Apply cyclic quadrilateral facts.
✓Combine tangent and chord theorems.
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The Wise Owl
Guides study flow, revision planning, and calmer focus sessions.
Practice setQuestion lineup
Try each question first, reveal a hint when you need one, then check the worked answer. Mark them done as you go — finish the set to claim your chips.
8 revision questions
Question 2FluencyCore
Original practice · Free Online RevisionSkill · semicircle theorem
AB is a diameter. C is on the circle. Find ∠ACB.
Question 3FluencyCore
Original practice · Free Online RevisionSkill · cyclic quadrilateral
In a cyclic quadrilateral, one angle is 112°. Find the opposite angle.
Question 4FluencyCore
Original practice · Free Online RevisionSkill · same segment
Two angles at the circumference stand on the same chord AB. One is 47°. Find the other if both vertices lie in the same segment.
Question 5FluencyCore
Original practice · Free Online RevisionSkill · tangent-chord theorem
A tangent at A makes angle 38° with chord AB. Find the angle in the alternate segment subtended by chord AB.
Question 6ReasoningCore
Original practice · Free Online RevisionSkill · tangent geometry
From P, PA and PB are tangents to a circle. If ∠APB=64°, find ∠AOB where O is the centre.
Question 7ReasoningStretch
Original practice · Free Online RevisionSkill · proof
Prove that opposite angles of a cyclic quadrilateral sum to 180°.
Question 8ChallengeStretch
Original practice · Free Online RevisionSkill · multi-theorem
In cyclic quadrilateral ABCD, tangent at A makes 52° with AB and ∠BAD=71°. Find ∠BCD and ∠ADB.