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Circle Theory

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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.

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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!**

Center of Circle Diameter

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