Question

1. How many tangents can a circle have?
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
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) V119 cm.
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 1

Answer:

1. 0 tangents

Exactly 0 tangents can be drawn through a circle. A tangent intersects a circle in only one point so it does not actually enter the area of the circle. An infinite number of tangents to a given circle can be drawn since their is no limit to the points a tangent could intersect.

2. fill in the blank

(a) one

A tangent of a circle intersects the circle exactly in one single point.

(b) secant

It is a line that intersects the circle at two points.

(c) Two,

There can be only two parallel tangents to a circle.

(d) point of contact

The common point of a tangent and a circle.

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Answer 2

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.

(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.

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) √119 cm  ..... right option

the line that is drawn from the centre of the given circle to the tangent PQ is perpendicular to PQ.

And so, OP ⊥ PQ

Using Pythagoras theorem in triangle ΔOPQ we get,

OQ2 = OP2+PQ2

(12)2 = 52+PQ2

PQ2 = 144-25

PQ2 = 119

PQ = √119 cm

So, option D i.e. √119 cm is the length of PQ.

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

XY and AB are two the parallel lines. The line segment AB is the tangent at point C while the line segment XY is the secant.