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The perpendicular bisector of a chord passes through the centre of the circle
O
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O
The perpendicular bisector of a chord passes through the centre of the circle
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O
The perpendicular bisector of a chord passes through the centre of the circle
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Finding the Centre of Rotation
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The shapes below have been produced by rotation.Find the centre of rotation
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The shapes below have been produced by rotation.Find the centre of rotation
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The shapes below have been produced by rotation.Find the centre of rotation
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The shapes below have been produced by rotation.Find the centre of rotation
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O
Inscribed angles which correspond to the same arc are equal
Inscribed Angle
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O
Inscribed angles which correspond to the same arc are equal
Does this inscribed angle correspond to the same arc?
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A central angle is twice as large as any inscribed angle which corresponds to the same arc
Central Angle
Inscribed Angle
O
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Various Forms of the Theorem
O
O
O
OO
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O
An inscribed angle which corresponds to a diameter (or semicircle) is a right angle
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O Cyclic Quadrilateral
Opposite angles in a cyclic quadrilateral are supplementary
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O
Tangent
Tangent point
A tangent and a radius drawn at any point on the circumference of the circle meet at right angles
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O
The intersection of two tangents to a circle is equidistant from their points of contact.
[Their angle of intersection and the central angle formed by the radii at the points of contact, are supplementary]
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O
The angle formed by a chord and a tangent at one of its endpoints is equal to the inscribed angle corresponding to the same chord in the alternating segment
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50°
a
b
130°
25°
25°
Can you solve this problem without a circle theorem?
O
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57°
t
O
r123°
57°
Can you think of another reason as to why both these angles are 57° ?