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Circle theorems

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• 1.
• 2. MR. DEEPAK KUMAR
• Circle Theorems
• 3. 2x x 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. This is the ARC o Centre of Circle
• 4. 2x x o Angle subtended at the Centre is twice the angle at the circumference Case 2 This is the ARC Centre of Circle
• 5. Angles Subtended in the same segment of a circle are equal Chop Sticks x x x We are ALL EQUAL This is the Arc Minor Segment Major Segment
• 6. A B C D 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. o x 180- x If this angle was 60 0 then angle BCD would be 180 0 -60 0 =120 0 120 0
• 7. Tangents T A B O TA=TB NB Triangles OBT and OAT are CONGRUENT! Tangent Tangent
• 8. 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 Major Segment Minor Segment
• 9. Diameter The angle in a semi circle is 90 degrees! Centre of Circle