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CBSE 10th Maths - Circles-Exercise-10.1

Question 1 How many tangents can a circle have?
Solution:

There can be infinite tangents to a circle. A circle is made up of infinite points which are at an equal distance from a point.

Since there are infinite points on the circumference of a circle, infinite tangents can be drawn from them.

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) A tangent to a circle intersects it in one point(s).

(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 the 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:

In the above figure, the line that is drawn from the center of the given circle to the tangent PQ is perpendicular to PQ.

And so, OP $\bot$ PQ

Using Pythagoras’ theorem in triangle ΔOPQ, we get,

$OQ^{2}$ = $OP^{2}+PQ^{2}$

$(12)^{2}$ =$5^{2}+PQ^{2}$

$PQ^{2}$= 144-25

$PQ^{2}$ = 119

PQ = $\sqrt{119}$ cm

So, option D, i.e., $\sqrt{119}$ cm, is the length of PQ.

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:

In the above figure, XY and AB are two parallel lines. Line segment AB is the tangent at point C, while line segment XY is the secant.

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