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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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