**Circles Class 9 Worksheets with Answers**

**Circles Class 9 Worksheets** play a vital role in strengthening the maths
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the students by giving them these **Circles Class 9 Worksheets** to solve.

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**Circles Class 9 Worksheet 1**

**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**

**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:

a. radius b. diameter

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.

**ANSWERS**

**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°

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