CHAPTER 11
CIRCLE
RECAPITULATION OF CONCEPTS LEARNT IN IX STANDARD
| 1. | Equal chords subtend equal angles at the centre of the circle. |
| 2. | Equal chords of congruent circles subtend equal angles at the centre of the circle. |
| 3. | Equal chords of a circle are equidistant from the centre of the circle. |
| 4. | Equal chords of congruent circles are equidistant from their corresponding centres. |
| 5. | If two chords of a circle are considered, the chord nearer to the centre is larger. |
| 6. | The perpendicular drawn from the centre of a circle bisects the chord. |
| 7. | Angles in the same segment of a circle are equal. |
| 8. | Angle subtended by an arc at the centre of a circle is double the angle subtended at any other point on the remaining part of the circle. |
| 9. | Angle in a semicircle is a right angle. |
| 10. | If the four vertices of a quadrilateral lie on a circle, it is a cyclic quadrilateral. |
| 11. | The opposite angles of a cyclic quadrilateral are supplementary (their sum is 180°). |
| 12. | If one side of a cyclic quadrilateral is produced, then the exterior angle is equal to the interior opposite angle. |
CONCEPTS IN X STANDARD
| 1. | Tangent is a line which intersects a circle at only one point. |
| 2. | Secant is a line which intersects a circle at two points. |
| 3. | From a point inside the circle, no tangent can be drawn to that circle. |
| 4. | From a point on the circle, only one tangent can be drawn to the circle. |
| 5. | From a point outside the circle, two tangents can be drawn to the circle. |
