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Hint

1

1

The angle at the centre of a circle is twice the angle at the circumference when both subtended by the same arc

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2

2

Every angle subtended at the circumference of a semicircle by the diameter is a right angle

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3

3

Angles subtended at the circumference in the same segment of a circle are equal

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4

4

The sum of the opposite angles of a cyclic quadrilateral is equal to 180*

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5

5

A tangent to a circle is perpendicular to the radius drawn to the point of contact

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6

6

Tangents to a circle from an external point to the points of contacts are equal

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7

7

The line joining an external point to the centre of the circle bisects the angle between the tangents

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8

8

A radius bisects a chord at 90* and 0 is the centre of the circle

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9

9

Alternate segment theorem

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