The document discusses several circle theorems including: 1) The angle subtended at the center of a circle by an arc is twice the size of the angle on the circumference subtended by the same arc. 2) Angles subtended in the same segment of a circle are equal. 3) A cyclic quadrilateral is a quadrilateral with all four vertices lying on the same circle.

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