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Published byPierre Love Modified about 1 year ago

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Draw and label on a circle: Centre Radius Diameter Circumference Chord Tangent Arc Sector (major/minor) Segment (major/minor)

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a a a r r Circle Fact 1. Isosceles Triangle Any triangle AOB with A & B on the circumference and O at the centre of a circle is isosceles.

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Circle Fact 2. Tangent and Radius The tangent to a circle is perpendicular to the radius at the point of contact.

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Circle Fact 3. Two Tangents The triangle produced by two crossing tangents is isosceles.

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Circle Fact 4. Chords If a radius bisects a chord, it does so at right angles, and if a radius cuts a chord at right angles, it bisects it.

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Circle Theorem 1: Double Angle The angle subtended by an arc at the centre of a circle is twice the angle subtended at the circumference.

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Circle Theorem 2: Semicircle The angle in a semicircle is a right angle.

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Circle Theorem 3: Segment Angles Angles in the same segment are equal.

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Circle Theorem 4: Cyclic Quadrilateral The sum of the opposite angles of a cyclic quadrilateral is 180 o.

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Circle Theorem 5: Alternate Segment The angle between a chord and the tangent at the point of contact is equal to the angle in the alternate segment.

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Circle Theorem 1: Double Angle The angle subtended by an arc at the centre of a circle is twice the angle subtended at the circumference.

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a a b b b 180 – 2a 2a + 2b = 2(a + b)

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Circle Theorem 2: Semicircle The angle in a semicircle is a right angle.

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180 – 2a 180 – 2b a a b b 360 – 2(a + b) = = 2(a + b) 90 = (a + b)

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Circle Theorem 3: Segment Angles Angles in the same segment are equal.

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a a 2a

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Circle Theorem 4: Cyclic Quadrilateral The sum of the opposite angles of a cyclic quadrilateral is 180 o.

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a b 2a 2b 2a + 2b = 360 2(a + b) = 360 a + b = 180

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Circle Theorem 5: Alternate Segment The angle between a chord and the tangent at the point of contact is equal to the angle in the alternate segment.

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a 90 - a 180 – 2(90 – a) 180 – a 2a a

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Double AngleSemicircle Segment Angles Cyclic Quadrilateral Alternate Segment

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