Circles Class 9 Worksheets

# Circles Class 9 Worksheets

Circles Class 9 Worksheets play a very important role in strengthening the maths concepts.

## Circles Class 9 Worksheet 1 with Answers

1.     In a circle of radius 17 cm, find the length of a chord which is 15 cm apart from the centre.

2.     Find BOC in the given figure.

3.     In the given figure, find AOB.

4.     In the given figure, AB is the diameter of a circle and ABCD is an isosceles trapezium. If CAB = 25°, find ADC.

5.     In a circle with centre O, OM perpendicular AB, If OM = 3 cm and the length of the chord is 8 cm, then find the radius of the circle.

6.     In the given figure, AOB is the diameter and BAC = 42°. Find the angle marked as x.

7.     In the given figure, AB || CD, CAB = 20° and ACB = 70°. Find CPD.

8.     Find the angle marked as x and y in the given figure.

9.     In the given figure, find the angle marked as x.

10.  In the given figure, AC is the diameter of a circle with centre O. If AOB = 40°, find the angle marked as x and y.

11. Find x, y and z in the given figure.

12. Find the marked angles.

## Circles Class 9 Worksheet 2 with Answers

1. Find the length of a chord which is at a distance of 5 cm from the centre of a circle of radius 13 cm.

2. In the given figure, identify:

c. chord                d. segment

e. sector                f. arc

g. exterior points   h. interior points

3. Î”PQR is inscribed in a circle with centre O and QR is a diameter. If PQR = 65°, find PRQ.

4. Fill in the blanks.

a. All points lying inside/outside a circle are called _______ points/_______ points.

b. The longest chord of a circle is the _______ of the circle.

c. Segment of a circle is the region between an arc and _______ of the circle.

d. Circles having the same centre and different radii are called _______ circles.

e. _______ is the arc from one end of a diameter to the other end.

5. In the given figure, identify:

a. secants of the circle

b. diameter of the circle

c. tangents to the circle

6. In the given figure, calculate ABC. (Hint: Join OB as radius)

7. Prove that any two tangents drawn from an external point to a circle with centre O are equal.

8. AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24 cm. If the chords are on the opposite sides of the centre and the distance between them is 17 cm, find the radius of the circle.

9. A tangent of 4 cm is drawn to a circle with centre O and the point outside is joined with centre which measures 5 cm. Find the radius of the circle.

10. A circle with centre O has radius 8 cm. A point X is taken outside the circle touching the circle at Y. If XY = 15 cm long, find the distance of X from the centre of the circle.

11. Find x from the given figure and then give measures of A, B and C.

12. A chord AB of a circle is equal to the radius (r) of the circle. Find all the angles subtended by joining the ends of chord to the centre.

Worksheet 1

1. 16 cm          2. 120°

3. 80°               4. 115°

5. 5 cm            6. x = 42°

7. 140°

8. x = 35°; y = 95°

9. 55°

10. x = 20°; y = 20°

11. x = 65°; y = 15°; z = 90°

12. a. x = 45°; y = 45°

b. x = 130°

Worksheet 2

1. 24 cm

2. a. OP, OQ, OR

b. PQ          c. AB

d. APBA     e. ROQR

f. RQ           g. T, U

h. S, O

3. 25°

4. a. interior; exterior

b. diameter

c. a chord

d. concentric

e. semicircle

5. a. AB, PQ, RQ, RS

b. MN

c. l, m

6. 70°

7. Do it yourself

8. 13 cm        9. 3 cm

10. 17 cm

11. A = 58°; B = 90°; C = 32°

12. Each angle is 60°