Exercise 10.1 (Revised) - Chapter 10 - Circles - Ncert Solutions class 10 - Maths

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Chapter 10: Circles - NCERT Solutions for Class 10 Maths

Ex 10.1 Question 1.

How many tangents can a circle have?

Answer.

A circle can have infinitely many tangents since there are infinitely many points on the circumference of the circle and at each point of it, it has a unique tangent.
Ex 10.1 Question 2.

Fill in the blanks:
(i) A tangent to a circle intersects it in $\qquad$ point(s).
(ii) A line intersecting a circle in two points is called a $\qquad$
(iii) A circle can have $\qquad$ parallel tangents at the most.
(iv) The common point of a tangent to a circle and the circle is called $\qquad$
Answer.

(i) A tangent to a circle intersects it in exactly one point.
(ii) A line intersecting a circle in two points is called a secant.
(iii) A circle can have two parallel tangents at the most.
(iv) The common point of a tangent to a circle and the circle is called point of contact.
Ex 10.1 Question 3.

A tangent $P Q$ at a point $P$ of a circle of radius $5 \mathrm{~cm}$ meets a line through the centre $O$ at a point $Q$ so that $O Q=12 \mathrm{~cm}$. Length $P Q$ is:
(A) $12 \mathrm{~cm}$
(B) $13 \mathrm{~cm}$
(C) $8.5 \mathrm{~cm}$
(D) $\sqrt{119} \mathrm{~cm}$

Answer.

(D) $\because P Q$ is the tangent and $O P$ is the radius through the point of contact.
$\therefore \angle \mathrm{OPQ}=90^{\circ}$ [The tangent at any point of a circle is $\perp$ to the radius through the point of contact]
$\therefore$ In right triangle $\mathrm{OPQ}$,

$\mathrm{OQ}^2=\mathrm{OP}^2+\mathrm{PQ}^2$ [By Pythagoras theorem]
$
\begin{aligned}
& \Rightarrow(12)^2=(5)^2+P Q^2 \\
& \Rightarrow 144=25+P Q^2 \\
& \Rightarrow P Q^2=144-25=119 \\
& \Rightarrow P Q=\sqrt{119} \mathrm{~cm}
\end{aligned}
$
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.

Answer: