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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