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Hint

Circle Theorem, both IGCSE & GCSE Maths (Edexcel)

1

Angles at the centre

Angle at the centre is twice the angle at the circumference

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2

Angles in the same segment

Angles in the same segment are equal.

Angles *a = a*

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3

Angle in a semicircle

The angleĀ in aĀ semicircle is 90Ā° or a right angle

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4

What is a cyclic quadrilateral?

AĀ **cyclic quadrilateral**Ā is aĀ **quadrilateral**Ā drawn inside a circle. Every corner of the quadrilateral must touch theĀ **circumference**Ā of the circle.

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5

Tangents

There are two circle theorems involvingĀ **tangents**.

1. The angle between a tangent and aĀ **radius**Ā is 90Ā°.

2. Tangents which meet at the same point are equal in length.

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6

Chords

The perpendicular from the centre of a circle to aĀ **chord**Ā **bisects**Ā the chord.

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7

The alternate segment theorem

The angle between aĀ **tangent**Ā and aĀ **chord**Ā is equal to the angle in the alternate segment.

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8

Two Tangent Theorem

if two tangent segments are drawn to one circle from the same external point, then they are congruent.

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