circles class 10 ncert solution,artic circle, circle lines , ncert solutions, chapter 10,chapter 10ncert solutions, circles ncert solutions, ncert solutions for class 10 maths, class 10 maths ncert solutions, ncert solutions for class 10, ncert class 10 maths, class 10 maths, class 10 maths solution, ncert solutions class 10, class 10 maths , ncert class 10, class 10 maths chapter 10,chapter 10 circles ncert solutions

EXERCISE 10.1

**Question 1.** How many tangents can a circle have?
2. Fill in the blanks :

(i) A tangent to a circle intersects it in point (s).

(ii) A line intersecting a circle in two points is called a .

(iii) A circle can have parallel tangents at the most.

(iv) The common point of a tangent to a circle and the circle is called .

**Question 2.** A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at
a point Q so that OQ = 12 cm. Length PQ is :

(A) 12 cm

(B) 13 cm

(C) 8.5 cm

(D) 119 cm.

**Question 3.** Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.

EXERCISE 10.2

**Question 1.** From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from
the centre is 25 cm. The radius of the circle is

(A) 7 cm

(B) 12 cm

(C) 15 cm

(D) 24.5 cm

**Question 2.** In Fig. 10.11, if TP and TQ are the two tangents
to a circle with centre O so that ∠ POQ = 110°,
then ∠ PTQ is equal to

(A) 60°

(B) 70°

(C) 80°

(D) 90°

**Question 3.** If tangents PA and PB from a point P to a circle with centre O are inclined to each other
at angle of 80°, then ∠ POA is equal to

(A) 50°

(B) 60°

(C) 70°

(D) 80°

**Question 4.** Prove that the perpendicular at the point of contact to the tangent to a circle passes
through the centre.

**Question 5.** The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4
cm. Find the radius of the circle.

**Question 6.** Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the
larger circle which touches the smaller circle.

**Question 7.** A quadrilateral ABCD is drawn to circumscribe a circle (see Fig. 10.12). Prove that
AB + CD = AD + BC
Fig. 10.12 Fig. 10.13

**Question 8.** In Fig. 10.13, XY and X′Y′ are two parallel tangents to a circle with centre O and
another tangent AB with point of contact C intersecting XY at A and X′Y at B. Prove
that ∠ AOB = 90°.

**Question 9.** Prove that the angle between the two tangents drawn from an external point to a circle
is supplementary to the angle subtended by the line-segment joining the points of
contact at the centre.

**Question 10.** Prove that the parallelogram circumscribing a
circle is a rhombus.

**Question 11.** A triangle ABC is drawn to circumscribe a circle
of radius 4 cm such that the segments BD and
DC into which BC is divided by the point of
contact D are of lengths 8 cm and 6 cm
respectively (see Fig. 10.14). Find the sides AB
and AC.

**Question 12.** Prove that opposite sides of a quadrilateral
circumscribing a circle subtend supplementary
angles at the centre of the circle.

Please Wait pdf file is loading **(कृपया इंतजार करें pdf file लोड हो रही है)...**

Loading speed will depend up on your download speed. **Pdf file के लोड होने में लगा समय आपकी डाउनलोड ���्पीड पर निर्भर करेगा **

Loading document ...

Loading page ...

To download above pdf file Link is **given below**.

उपर दिखायी दे रही पीडीऍफ़ को डाउनलोड करने का लिंक**नीचे दिया गया है **

उपर दिखायी दे रही पीडीऍफ़ को डाउनलोड करने का लिंक

- Chapter 1: REAL NUMBERS
**[Ques wise Ans]** - Chapter 2: POLYNOMIALS
**[Ques wise Ans]** - Chapter 3: PAIR OF LINEAR EQUATIONS IN TWO VARIABLE
**[Ques wise Ans]** - Chapter 6: Triangles
**[Ques wise Ans]** - Chapter 3 Pair of Linear Equations in Two Variables
- Chapter 4 Quadratic Equations
- Chapter 7 Coordinate Geometry
- Chapter 8 Introduction to Trigonometry
- Chapter 11 Constructions
- Chapter 9 Some Applications of Trigonometry
- Chapter 10 Circles
- Chapter 12 Areas Related to Circles
- Chapter 13 Surface Areas and Volumes
- Chapter 14 Statistics
- Chapter 15 Probability
- Chapter 5 Arithmetic Progressions

- NCERT Solutions for Class 9
- NCERT Solutions for Class 10
- NCERT Solutions for Class 11
- NCERT Solutions for Class 12

If You have any problem/query related to above page please send us your Query to ncerthelp@gmail.com with code **Serial No1481/1103**. Thanks

Copyright @ ncerthelp.com A free educational website for CBSE, ICSE and UP board.