The angle at the centre (AOB) is twice the angle at the circumference (APB). As AOB is 180°, it follows that APB is 90°. AOB is the diameter, so it follows that the angle in a semicircle is always a right angle.

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Angles in the same segment are equal

Angles subtended (made) by the same arc at the circumference are equal.

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The angle at the centre of a circle

the angle subtended at the centre of a circle is double the size of the angle subtended(made/hanging down) at the edge from the same two points

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Opposite angles in a cyclic quadrilateral add up to 180°

A cyclic quadrilateral is a quadrilateral whose vertices all touch the circumference of a circle. The opposite angles add up to 180. In the cyclic quadrilateral below, angles A + C = 180.

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The perpendicular from the centre to the chord bisects the chord

In the diagram below, AB is the chord of a circle with centre O. OM is the perpendicular from the centre to the chord.

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The angle between the tangent and radius is 90°

A tangent is always at right angles to the radius where it touches the circle.

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Tangents from a point outside the circle are equal in length

Two tangents to a circle from a point are equal.

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Alternate segment theorem

The angle between the tangent and chord at the point of contact is equal to the angle in the alternate segment.

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Other cards in this set

Card 2

Front

Angles subtended (made) by the same arc at the circumference are equal.

Back

Angles in the same segment are equal

Card 3

Front

the angle subtended at the centre of a circle is double the size of the angle subtended(made/hanging down) at the edge from the same two points

Back

Card 4

Front

A cyclic quadrilateral is a quadrilateral whose vertices all touch the circumference of a circle. The opposite angles add up to 180. In the cyclic quadrilateral below, angles A + C = 180.

Back

Card 5

Front

In the diagram below, AB is the chord of a circle with centre O. OM is the perpendicular from the centre to the chord.

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