**CBSE Class 10 Maths Chapter 10 Important Questions:** In this article we will be covering the various sorts of important questions and answers from Chapter 10th of CBSE Class 10 Mathematics syllabus. Chapter 10 Circles is a part of the fourth unit Geometry.

The topics covered in this chapter are:

Tangent to a circle at, point of contact

- (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.
- (Prove) The lengths of tangents drawn from an external point to a circle are equal.

To view the complete curriculum, check **CBSE Class 10 Maths Syllabus 2022-2023**.

**CBSE Class 10 Maths Chapter 10 Important Questions**

We would first begin with the MCQs and then move on with the very short answer type questions, short answer type questions, long answer type questions and at last, case study questions.

**MULTIPLE CHOICE QUESTIONS**

- In Fig. if from an external point T, TP and TQ are two tangents to a circle with centre O so that < POQ = 110O, then < PTQ is:

- 60 degree
- 70 degree
- 80 degree
- 90 degree

2. In the fig. if the semi perimeter of ∆ABC = 23cm, then AF + BD + CE is:

- 46cm
- 11.5cm
- 23cm
- 34.5cm

- In fig. AQ, AR and BC are tangents to a circle with centre O, If AB = 7cm, BC = 5cm AC = 5cm, then the length of tangent AQ is:

- 5cm
- 7cm
- 8.5cm
- 17cm

4. In the fig. PT is a tangent to a circle with centre O. If PT = 30 cm and diameter of circle is 32cm, then the length of the line segment OP will be:

- 68cm
- 34cm
- 17cm
- 34.8cm

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

- 3/2 (√3) cm
- 6 cm
- 3 cm
- 3√3 cm

- The distance between two parallel tangents to a circle of radius 5cm is:

- 10cm
- 11cm
- 12cm
- 14cm

7. If the circumference of a circle increases from 4π to 8π, then its area will become

- half
- 2 times
- 4 times
- does not change

- If two tangents inclined to each other at an angle 60O are drawn to a circle of radius 3cm, then the length of tangent is equal to:

- √3 cm
- 2√3 cm
- 2/√3 cm
- 3√3 cm

- A line which is perpendicular to the radius of the circle through the point of contact is:

- Tangent
- Chord
- segment
- normal

- Number of tangents to a circle which are parallel to a secant is:

- 1
- 2
- 3
- Infinite

- Maximum number of common tangents that can be drawn to two circles intersecting at two distinct points is:

- 1
- 2
- 3
- 4

- From a point P which is at a distance of 13cm from the centre O of a circle of radius 5cm, the pair of tangents PQ and PR to the circle are drawn. What are the lengths (in cm) of tangents PQ and PR?
- 13,12
- 13, 13
- 12,12
- 12,18

**VERY SHORT ANSWER QUESTIONS**

- Prove that the line segments joining the points of contact of two parallel tangents is a diameter of the circle.
- Two concentric circles have centre O, OP= 4cm, OB = 5cm. AB is a chord of the outer circle and tangent to the inner circle at P. Find the length of AB.
- In the isosceles triangle ABC in fig. AB = AC, show that BF = FC

Two tangents PA and PB are drawn to a circle with centre O such that < APB = 1200. Prove that OP=2AP

- In the fig. a circle is inscribed in a ∆ABC with sides AB = 12cm, BC = 8 cm and AC = 10cm. Find the lengths of AD, BE and CF
- In fig. circle is inscribed in a quadrilateral ABCD in which < B= 900. If AD = 23cm, AB = 29cm, and DS = 5cm, find the radius ‘r’ of the circle
- Two tangents PR and PQ are drawn from external point P to a circle with centre O. Prove that PROQ is a cyclic quadrilateral.
- Prove that tangents drawn at the ends of a chord make equal angles with the chord
- Two concentric circles are of radii 7 cm and r cm respectively, where r > 7. A chord of the larger circle, of length 48 cm, touches the smaller circle. Find the value of r
- In the given figure, AP and BP are tangents to a circle with centre O, such that AP = 5cm, APB = 60O. Find the length of chord AB.
- In the figure quadrilateral ABCD is drawn to circumscribe a circle.

Prove that AD + BC = AB + CD

**SHORT ANSWER QUESTIONS**

- If an angle between two tangents drawn from a point P to a circle of radius ‘a’ and centre O is 60°, then prove that AP = a√3.
- If all the sides of a parallelogram touch a circle, then prove that the parallelogram is a rhombus.
- XY and X1Y1 are two parallel tangents to a circle with centre O and another tangent AB with point of contact C, intersecting XY at A and X1Y1 at B, is drawn. Prove that ∠AOB = 90°.
- Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that

∠PTQ=2 * ∠OPQ.

- Prove that the parallelogram circumscribing a circle is a rhombus.

**LONG ANSWER QUESTIONS**

- Prove that the lengths of tangents drawn from an external point to a circle are equal.
- The radius of the in-circle of a triangle is 4 cm and the segments into which one side is divided by the point of contact are 6 cm and 8 cm. Determine the other two sides of the triangle.

**CASE STUDY BASED QUESTIONS**

- People of the village want to construct a road nearest to the circular village Parli. The road cannot pass through the village. But the people want the road to be at the shortest distance from the centre of the village. Suppose the road starts from point O which is outside the circular village and touches the boundary of the circular village at point A such that OA = 20 m. And also, the straight distance of the point O from the center C of the village is 25 m.

1. Find the shortest distance of the road from the centre of the village

a) 15m

b) 14m

c) 13m

d) 12m

2. Which method should be applied to find the shortest distance?

a) Concept of tangent to a circle

b) Pythagoras theorem

c)Both a and b

d) None of these

3. If a point is inside the circle, how many tangents can be drawn from that point

a) 0

b) 1

c) 2

d) 3

4. Number of common tangents can be drawn to two circles which do not intersect

a) 2

b) 3

c) 4

d) 1

5. If we draw two tangents at the end of the diameter, these tangents are always

a) Parallel

b) perpendicular

c) coincident

d) None of these

- Varun has been selected by his School to design logo for Sports Day T-shirts for students and staff. The logo design is as given in the figure and he is working on the fonts and different colours according to the theme. In given figure, a circle with centre O is inscribed in a ΔABC, such that it touches the sides AB, BC and CA at points D, E and F respectively. The lengths of sides AB, BC and CA are 12 cm, 8 cm and 10 cm respectively.

- Find the length of AD

a) 7

b) 8

c) 5

d) 9

2. Find the Length of BE

a) 8

b) 5

c) 2

d) 9

3. Find the length of CF

a) 9

b) 5

c) 2

d) 3

4. If radius of the circle is 4 cm, Find the area of ΔOAB

a) 20

b) 36

c) 24

d) 48

5. Find area of ΔABC

a) 50

b) 60

c) 100

d) 90

To view the answers, click on the link below:

**CBSE Class 10 Maths Chapter 10 Important Questions with Answers: CIRCLES**

The other chapter in this unit is Triangles.

Together, Chapter 6 Triangles and Chapter 10 Circle, have a total weightage of 15 marks.

To understand more about what other kinds of questions can be asked from the complete syllabus for CBSE Class 10 Mathematics examination 2022-23, check CBSE Class 10 Mathematics sample question papers for the current academic year.

*CBSE Class 10 Mathematics Standard Sample Paper 2023*

* CBSE Class 10 Mathematics Basic Sample Paper 2023*

All the best!