Chapter 10 Circles Exercise-01
EXERCISE 10.1
1. How many tangents can a circle have?
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Solution
A circle can have infinite tangents.
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 _______.
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Solution
(i) One
(ii) Secant
(iii) Two
(iv) Point of contact
3. A tangent $\mathrm{PQ}$ at a point $\mathrm{P}$ of a circle of radius $5 \mathrm{~cm}$ meets a line through the centre $\mathrm{O}$ 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) $\sqrt{119} \mathrm{~cm}$.
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Solution
We know that the line drawn from the centre of the circle to the tangent is perpendicular to the tangent.
$\therefore OP \perp PQ$
By applying Pythagoras theorem in $\triangle OPQ$,
$\therefore OP^{2}+PQ^{2}=OQ^{2}$
$5^{2}+PQ^{2}=12^{2}$
$PQ^{2}=144-25$
$PQ=\sqrt{119} cm$.
Hence, the correct answer is (D).
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.
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Solution
It can be observed that $A B$ and $C D$ are two parallel lines. Line $A B$ is intersecting the circle at exactly two points, $P$ and $Q$. Therefore, line $A B$ is the secant of this circle. Since line $C D$ is intersecting the circle at exactly one point, $R$, line $C D$ is the tangent to the circle.
