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Circle Theory.

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Presentation on theme: "Circle Theory."— Presentation transcript:

1 Circle Theory

2 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.

3 Case 2 Centre of Circle x o 2x This is the ARC
Angle subtended at the Centre is twice the angle at the circumference

4 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

5 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

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

7 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

8 The angle in a semi circle is 90 degrees!
Center of Circle Diameter


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