Q2 of 12 Page 164

Fill in the blanks:

(i) Through a point on a circle…………………… tangent lines can be drawn.


(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…………….. .

(i) Through a point on a circle one tangent lines can be drawn.



Let the centre be O.


From this figure it can be interpreted that OP will be the radius of the circle.


For the line LM which contains the point P, the distance OP<OL because OP is the perpendicular distance and perpendicular distance is always the shortest distance.


OP is perpendicular to LP and MP.


This is possible only when all the L, P and M lie on same line.


Hence LPM is a straight line.


LM is the only tangent which pass through the point P.


Hence only one tangent can be drawn from a point on a circle.


(ii) A line intersecting a circle in two points is called a secant.



(iii) A circle can have two Parallel tangents at the most.


A tangent line touches a shape at a single point. Two parallel tangents will be on opposite sides of the circle. If you try to add another parallel line, it will pass through two points of the circle, and isn't a tangent.



(iv) The common point of a tangent to a circle and the circle is called point of contact or point of tangency.


In the above figure P is the point of contact for the tangent LM and Q is the point of contact for the tangent XY.


More from this chapter

All 12 →
1

Write true or false of each of the following statements. Also give reason for your answer.

(i) A tangent of a circle is that line which intersects the circle at two points.


(ii) A tangent XY touches a circle at a point P and Q is any other point on the tangent. If O is the centre of the circle then, OP = OQ.


(iii) Two tangent LM and XY are drawn respectively at two points P and Q on a circle. If PQ is the diameter than LM || XY.


(iv) The centre ‘O’ of a circle lies on another circle whose centre is ‘A’. If the circle with centre O passed through the points A and B such that AOB is a straight line, then the tangents drawn from the point B will pass through the points of intersection of the two points.

 3

Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

 4

The length of a tangent from a point at a distance of 10 cm from the centre of the circle is 4 cm. Find the radius of the circle.

 5

A circle with centre O touches all the four sides of a quadrilateral ABCD. If the point of contact divides AB in the ratio 3 : 1 and AB = 8 cm, then find the radius of the circle if it is given OA = 10 cm.