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Construct a pair of tangents to a circle of radius 4 cm which are inclined to each other at an angle of $60^{o}$ .

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To construct a pair of tangents to a circle of radius 4 cm which is inclined to each other at an angle of $60^{o}$ .

We must know that angle at the centre in double the angle between the tangents.

The angle subtended at the centre $=120^{o}$

Steps for construction:

(i) Draw a circle of radius 4 cm

(ii) Draw a radius $BO$

(iii) Draw an angle of $120^{o}$ from point $O$ and let the ray interact the perimeter of the circle at point $C$

(iv) Now draw a $90^{o}$ angle from point $B$

(v) Draw a $90^{o}$ angle from point $C$

(vi) When we will extend the rays from point $B$ and point $C$ they will meet at point $A$

(vii) We get the required angles $AC \: and \; AB$ with angle of $60^{o}$ between them.

Justification :

$ABOC$ is a quadrilateral hence some of the external angles should be equal to $360^{o}$

$\Rightarrow \angle A+\angle B+\angle O+\angle C=360^{o}$

$\Rightarrow \angle A+90^{o}+120^{o}+90^{o}=360^{o}$

$\Rightarrow \angle A+300^{o}=360^{o}$

$\Rightarrow \angle A=60^{o}$

Hence justified the angle between tangents is $60^{o}$

Posted by

Safeer PP

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