Edexcel IGCSE·Mathematics 4MA1
Circle Theorems
Key knowledge — Geometry
Formulas & equations
Angles in a triangle: sum = 180°Angles in a quadrilateral: sum = 360°Exterior angle of a triangle = sum of the two non-adjacent interior anglesInterior angle of regular n-gon = (n−2) × 180° ÷ nExterior angle of regular n-gon = 360° ÷ nArc length = (θ/360) × 2πrArea of sector = (θ/360) × πr²
Key facts & rules
- Corresponding angles are equal (parallel lines, F-shape).
- Alternate angles are equal (parallel lines, Z-shape).
- Co-interior (allied) angles add up to 180° (parallel lines, C-shape).
- Tangent is perpendicular to radius at point of contact.
- Angle in semicircle = 90° (angle in a semicircle theorem).
- Angle at centre = 2 × angle at circumference (same arc).
- Angles in the same segment are equal.
- Opposite angles in a cyclic quadrilateral add to 180°.
- Similar shapes: all angles equal, sides in the same ratio. Area ratio = k², volume ratio = k³.
Laws & theorems
- Pythagoras: a² + b² = c² (right-angled triangles only).
- Congruence conditions: SSS, SAS, ASA, RHS.
Circle theorems
17 Edexcel IGCSE 4MA1 past paper questions on circle theorems — Foundation and Higher, with mark schemes.
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