Q4 of 12 Page 164

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.

Given:

Distance of point from center, OA = 10 cm


Length of tangent, AB = 4 cm.


Solution:


The diagram for the question is as follows:



Let the centre be O.


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


Radius OB is perpendicular to the tangent AB as radius is perpendicular to the tangent.


OB ⊥ AB


Hence Δ OAB is right angled triangle.


∠ OBA = 90°


By Pythagoras theorem,


OA2 = AB2 + OB2


OB2 = OA2 – AB2


OB2 = 102 – 42


OB2 = 100 – 16


OB2 = 84


OB2 = 21 × 2 × 2


OB = 2√21 cm


Therefore the radius of circle OB = 2√21 cm


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(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…………….. .

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