RBSE Solutions for Class 10 Maths Chapter 10 Circles Ex 10.1

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

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

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.

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.

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.