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RBSE Solutions for Class 10 Maths Chapter 10 Circles Ex 10.1

April 21, 2022 by Safia Leave a Comment

Rajasthan Board RBSE Solutions for Class 10 Maths Chapter 10 Circles Ex 10.1 Textbook Exercise Questions and Answers.

RBSE Class 10 Maths Solutions Chapter 10 Circles Exercise 10.1

Question 1.
How many tangents can a circle have?
Solution:
We know that one and only one tangent can be drawn at a point of a circle. But circle is the collection of infinitely many points, so we can drawn infinitely many tangents to a circle.

Question 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 ………….. .
Solution:
(i) one
(ii) secant
(iii) two
(iv) point of contact

RBSE Solutions for Class 10 Maths Chapter 10 Circles Ex 10.1

Question 3.
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) \(\sqrt {119}\) cm
Solution:
Drawing the figure according to the question
RBSE Solutions for Class 10 Maths Chapter 10 Circles Ex 10.1 1
OP = 5 cm. and OQ = 12 cm.
∵ PQ is a tangent and OP is a radius
∴ ∠OPQ = 90°
Now, in right △OPQ,
By Pythagoras Theorem,
OQ2 = OP2 + QP2.
(12)2 = (5)2 + QP2
QP2 = (12)2 – (5)2
QP2 = 144 – 25 = 119
QP = \(\sqrt {119}\) cm.
Hence, option (D) is correct.

RBSE Solutions for Class 10 Maths Chapter 10 Circles Ex 10.1

Question 4.
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.
Solution:
Let O be the centre of the given circle and PQ be a given line. We are required to draw the lines CD and AD parallel to PQ in which CD is a tangent and AB is a secant.
RBSE Solutions for Class 10 Maths Chapter 10 Circles Ex 10.1 2
Construction—

  1. Draw a perpendicular from centre point to the line PQ which intersects the circle at point C.
  2. A perpendicular CD has been drawn at point C of radius OC. Here CD is a tangent.
  3. Draw a perpendicular AB through a point M on OC. Then AB is a secant.

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