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**2x o Centre of Circle x This is the ARC**

The Angle x subtended at the centre of a circle by an arc is twice the size of the angle on the circumference subtended by the same arc. More Free powerpoints at

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**Case 2 Centre of Circle x o 2x This is the ARC**

Angle subtended at the Centre is twice the angle at the circumference

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**Angles Subtended in the same segment**

We are ALL EQUAL x Major Segment Chop Sticks Minor Segment This is the Arc Angles Subtended in the same segment of a circle are equal

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**Cyclic Quadrilateral A If this angle was 600 then angle**

BCD would be =1200 B o x 180-x D C 1200 Points which lie on the circumference of the same circle are called cyclic (or concyclic) points. A cyclic quadrilateral is a quadrilateral with all its four corners (vertices) on the circumference of the same circle. Cyclic Quadrilateral

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B Tangent O T A TA=TB Tangents NB Triangles OBT and OAT are CONGRUENT!

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E Major Segment D Minor Segment A B C The Shaded Segment BED is called the alternate segment to the angle CBD The angle between a tangent to a circle and a chord drawn through the point of contact is equal to any angle subtended by the chord at the circumference in the alternate segment

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**The angle in a semi circle is 90 degrees!**

Centre of Circle Diameter

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2. Chords are of equal length if and only if they are equidistant from the centre of circle.

2. Chords are of equal length if and only if they are equidistant from the centre of circle.

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