Circle Theorems
Year 10 (IGCSE) 📐 Geometry & Measures Apply circle theorems to find angles and prove results.
⭕ Key Circle Theorems
There are 8 key circle theorems to know for IGCSE.
Theorem 1: Angle at Centre
The angle at the centre is twice the angle at the circumference from the same arc.
Theorem 1
$$\angle AOC = 2 \times \angle ABC$$Theorem 2: Angle in Semicircle
The angle in a semicircle is always 90°.
Theorem 2
$$\angle \text{ in semicircle} = 90°$$Theorem 3: Angles in Same Segment
Angles in the same segment are equal.
Theorem 4: Cyclic Quadrilateral
Opposite angles in a cyclic quadrilateral add up to 180°.
Theorem 4
$$\angle A + \angle C = 180° \qquad \angle B + \angle D = 180°$$
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Interactive Demonstration — Circle Theorems
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