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Circle Theorems and Segment Relations in Geometry

Explore key circle theorems, angles subtended at the center and circumference, segment equality, cyclic quadrilaterals, tangent properties, and diameter angles in geometry. Understand relationships between different parts of a circle.

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Circle Theorems and Segment Relations in Geometry

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  1. Circle Theorems www.assignmentpoint.com

  2. Centre of Circle o This is the ARC x 2x 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. www.assignmentpoint.com

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

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

  5. If this angle was 600 then angle BCD would be 1800-600=1200 o 180-x x 1200 A B D C 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 www.assignmentpoint.com

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

  7. Major Segment Minor Segment E D A B C The Shaded Segment BEDis 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 www.assignmentpoint.com

  8. Centre of Circle The angle in a semi circle is 90 degrees! Diameter www.assignmentpoint.com

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