1
Understand circles
Describe a circle as all points at a fixed distance from a fixed point.
Chapter route
Circles
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Ordered curriculum items
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2
Know circle parts
Use circle terms correctly in diagrams and problems.
3
One circle through three points
Understand the uniqueness of a circle through three non-collinear points.
4
Draw a circumcircle
Use perpendicular bisectors to construct the circle through all three vertices.
5
Find the circumcentre location
Describe whether the circumcentre lies inside, outside or on a triangle.
6
Understand central angle
Connect an arc with the angle it forms at the circle centre.
7
Equal chords, equal angles
Justify the relationship between chord equality and central angles.
8
Equal angles, equal chords
Use congruence reasoning to prove the converse result.
9
Radius to chord midpoint
Show why the line from centre to chord midpoint is perpendicular.
10
Perpendicular bisects chord
Use circle symmetry or congruence to justify chord bisection.
11
Chord distance rule
Explain how chord length changes with distance from the centre.
12
Equal chords are equally distant
Justify the theorem and its converse.
13
Longest chord
Use distance from centre or geometry reasoning to compare chords.
14
Centre angle is double
Use the fact that an arc makes double angle at centre compared to circumference.
15
Same segment angles
Find or prove equal angles standing on the same arc.
16
Angle in semicircle
Apply the fact that the angle in a semicircle is a right angle.
17
Check concyclicity
Use circle properties to decide whether four points lie on one circle.
18
Use cyclic angle sums
Use supplementary opposite angles to solve cyclic quadrilateral problems.
19
Prove a quadrilateral is cyclic
Show concyclicity using supplementary opposite angles.
20
Circles in daily life
Connect circle geometry with transport, farming and machines.
21
Circles in culture
Recognise circle ideas in symbols such as Dharmachakra and Ashoka Chakra.
22
Choose the right circle theorem
Break a circle problem into diagram reading, theorem selection and calculation steps.
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