Circle Theorems and Angle Facts
Drag the points and watch every angle change. Then test yourself.
Every theorem and the reason to write in the exam
- Angle at the centre
- The angle at the centre is twice the angle at the circumference.
- Angles in the same segment
- Angles in the same segment are equal.
- Angle in a semicircle
- The angle in a semicircle is 90°.
- Cyclic quadrilateral
- Opposite angles in a cyclic quadrilateral add up to 180°.
- Tangent and radius
- A tangent meets a radius at 90°.
- Two tangents from a point
- Tangents from an external point are equal in length.
- Alternate segment
- The angle between a tangent and a chord is equal to the angle in the alternate segment.
- Chord bisector
- The perpendicular from the centre to a chord bisects the chord.
- Intersecting chords: insideIGCSE only
- AX × XB = CX × XD (intersecting chords).
- Intersecting chords: outsideIGCSE only
- PA × PB = PC × PD (intersecting chords).
- Alternate angles
- Alternate angles are equal.
- Corresponding angles
- Corresponding angles are equal.
- Co-interior angles
- Co-interior angles add up to 180°.
- Vertically opposite angles
- Vertically opposite angles are equal.
- Angles on a straight line
- Angles on a straight line add up to 180°.
- Angles at a point
- Angles around a point add up to 360°.
- Triangles
- Angles in a triangle add up to 180°. The exterior angle equals the sum of the two opposite interior angles.
- Isosceles triangle
- Base angles in an isosceles triangle are equal.
- Angles in a quadrilateral
- Angles in a quadrilateral add up to 360°.
- Interior angles
- Sum of interior angles = (n − 2) × 180°.
- Exterior angles
- Exterior angles of a polygon add up to 360°.
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