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Chapter 9: Circles > What We Have Discussed

What We Have Discussed

1. A collection of all points in a plane which are at a fixed distance from a fixed point in the same plane is called a . The fixed point is called the and the fixed distance is called the of the circle.

2. A line segment joining any points on the circle is called a .

3. The longest of all chords which also passes through the centre is called a .

4. Circles with the same radii are called .

5. Circles with the same centre and different radii are called .

6. The diameter of a circle divides it into two .

7. The part between any two points on the circle is called an .

8. The area enclosed by a chord and an arc is called a . If the arc is a minor arc, then it is called the segment, and if the arc is major, then it is called the segment.

9. The area enclosed by an arc and the two radii joining the endpoints of the arc with the centre is called a .

10. Equal chords of a circle subtend equal angles at the .

11. Angles in the same segment are .

12. An angle in a semi-circle is a .

13. If the angles subtended by two chords at the centre are equal, then the chords are .

14. The perpendicular from the centre of a circle to a chord bisects the . The converse is also .

15. There is exactly one circle passing through three points.

16. The circle passing through the vertices of a triangle is called a .

17. Equal chords are at equal distances from the of the circle; conversely, chords at equidistant from the centre of the circle are equal in .

18. An angle subtended by an arc at the centre of the circle is twice the angle subtended by it at any other point on the .

19. If the angle subtended by an arc at a point on the remaining part of the circle is 90°, then the arc is a .

20. If a line segment joining two points subtends the same angles at two other points lying on the same side of the line segment, the four points lie on the .

21. The pairs of opposite angles of a cyclic quadrilateral are .