2x x This is the ARC o Centre of Circle 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. By: manish yadav For better understanding

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

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

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o A B C D x 180- x If this angle was 60 0 then angle BCD would be 180 0 -60 0 =120 0 120 0 Cyclic Quadrilateral 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.

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

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Major Segment Minor Segment A B C E D 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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Centre of Circle Diameter The angle in a semi circle is 90 degrees!

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