**MCQs Questions for Class 10 Maths Chapter 10 Circles**

In this 21^{st} century, Multiple Choice Questions (MCQs) play a vital role to prepare for a competitive examination. CBSE board has also brought a major change in its board exam patterns. Now-a-days, a total of 10 MCQs questions are asked in the class 10 board examination.

In most of the competitive examinations, only MCQ questions are asked. So, for getting ready for the competitive examinations, we have to practice for MCQs questions to solve. It strengthens the critical thinking and problem solving skills.

In future, if you want to prepare for competitive examination and to crack it, then you should more focus on the MCQ questions. Thus, from the board examinations point of view and competitive examinations point of view, you should practice more on multiple choice questions.

Thus, let’s solve these MCQs Questions to make our foundation very strong.

**MCQs Questions for Class 10
Maths Chapter 10 Circles**

**1.** The
length of tangent from an external point P on a circle with centre O is

(A)
always greater than OP

(B)
equal to OP

(C)
always less than OP

(D) information insufficient

**Answer: C**

**2. **The distance between two
parallel tangents of a circle of radius 4 cm is

(A) 2 cm

(B) 4 cm

(C) 6 cm

(D) 8 cm

**Answer: D**

**3. **If radii of two concentric
circles are 4 cm and 5 cm, then the length of each chord of one circle which is
tangent to the other circle is

(A) 3 cm

(B) 6 cm

(C) 9 cm

(D) 1 cm

**Answer: B**

**4.** If
angle between two tangents drawn from a point P to a circle of radius ‘a’ and
centre ‘O’ is 90°, then OP =

(A)
2a√2

(B)
a√2

(C)
a/√2

(D) 5a√2

**Answer: B**

**5.** A tangent is drawn from a
point at a distance of 17 cm of circle C(0, r) of radius 8 cm. The length of
its tangent is

(A) 5 cm

(B) 9 cm

(C) 15 cm

(D) 23 cm

**Answer: C**

**6. **From a point P which is at a
distance of 13 cm from the point O of a circle of radius 5 cm, the pair of
tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral
PQOR is

(A) 60 cm²

(B) 65 cm²

(C) 30 cm²

(D) 32.5 cm²

**Answer: A**

**7.** At
one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to
the circle. The length of the chord CD parallel to XY and at a distance 8 cm
from A is

(A)
4 cm

(B)
5 cm

(C)
6 cm

(D) 8 cm

**Answer: D**

**8.** Number of tangents drawn at
a point of the circle is/are

(A) one

(B) two

(C) none

(D) infinite

**Answer: A**

**9. **If two tangents inclined at
an angle 60° are drawn to a circle of radius 3 cm, then the length of each
tangent is equal to

(A) 2√3
cm

(B) 6 cm

(C) 3 cm

(D) 3√3 cm

**Answer: D**

**10.** If
d_{1}, d_{2} (d_{2} > d_{1}) be
the diameters of two concentric circles and c be the length of a chord of a
circle which is tangent to the other circle, then

(A)
d_{2}^{2} = c^{2} + d_{1}^{2}

(B)
d_{2}^{2} = c^{2} - d_{1}^{2}

(C)
d_{1}^{2} = c^{2} + d_{2}^{2}

(D)
d_{1}^{2} = c^{2} - d_{2}^{2}

**Answer: A**

**11.** The tangents drawn at the
extremities of the diameter of a circle are

(A) perpendicular

(B) parallel

(C) equal

(D) none of these

**Answer: B**

**12.** The length of a tangent
drawn from a point at a distance of 10 cm of circle is 8 cm. The radius of the
circle is

(A) 4 cm

(B) 5 cm

(C) 6 cm

(D) 7 cm

**Answer: C**

**13.** If
a chord AB subtends an angle of 60° at the centre of a circle, then angle
between the tangents at A and B is:

(A)
60°

(B)
120°

(C)
80°

(D) 100°

**Answer: A**

**14. **C (O, r_{1}) and C(O,
r_{2}) are two concentric circles with r_{1} > r_{2},
AB is a chord of C(O, r_{1}) touching C(O, r,_{2}) at C, then

(A) AB = r_{1}

(B) AB = r_{2}

(C) AC = BC

(D) AB = r_{1} + r_{2}

**Answer: C**

**15.** Two parallel lines touch the
circle at points A and B respectively. If area of the circle is 25Ï€ cm^{2},
then AB is equal to

(A) 5 cm

(B) 8 cm

(C) 10 cm

(D) 25 cm

**Answer: C**