Circles Class 9 Notes Maths - Chapter 10

Chapter: 10

What Are Circles ?

Circle

The collection of all those points in a plane, which are equidistant from a fixed part in the same plane.

Concentric Circle

Circles having same centre and different radii.

TERMS RELATED TO CIRCLE

• CHORD — PQ

• MINOR ARC – PQ

• MAJOR ARC – PRO

• Area between PQ (Chord & Arc) = MINOR Segment

• Area between PQ Chord & Arc PRQ = MAJOR Segment

• Figure 2, Area between OA, OB & Arc AB = MINOR Sector

• AREA between OA, Arc ACB & OB = MAJOR Sector

1. Equal Chords of a circle subtends equal angles at the centre and vice versa.

2. Equal Chords of a circle are equidistant from the centre and vice versa.

3. The perpendicular drawn from the centre of the circle to a chord bisects the chord and vice versa.

4. The angle subtended by an arc at the centre is double the angle subtended by it at any other point on the circumference of the circle.

5. In a circle, angles in the same segment made by a chord are equal.

6. The angle in a semi-circle made by diameter (or largest chord) is right angle.

7. If two arcs of a circle are congruent, then their corresponding chords are equal and conversely if two chords of a circle are equal, then their corresponding areas are congruent.

8. It two circles intersect in two points, then the line through the centres is perpendicular to the common chord.

9. Congruent arcs of a circle subtend equal angles at the centre.

Cyclic Quadrilateral

CYCLIC QUADRILATERAL