NCERT Solutions Class 10 Mathematics Chapter 10 Circles Download In Pdf

Chapter 10 Circles Download in pdf

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.

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- 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

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