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# Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.

To do:

We have to draw a circle with the help of a bangle. Taking a point outside the circle, construct the pair of tangents from this point to the circle.

Solution:

__Steps of construction:__

(i) Draw a circle $C’$ with the help of a bangle, for finding the centre, take three non-collinear points $A, B$ and $C$, lying on the circle. Join $AB$ and $BC$ and draw perpendicular bisector of $AB$ and $BC$ which intersect at a point $O$.

$‘O’$ is centre of the circle.

(ii) Take a point $P$ outside the circle. Join $OP$.

(iii) Draw perpendicular bisector of $OP$, which intersects $OP$ at point $O’$.

(iv) Take $O’$ as the centre with $OO’$ as radius draw a circle which passes through $O$ and $P$, intersecting previous circle $C’$ at points $R$ and $Q$.

(v) Join $PQ$ and $PR$.

Therefore,

$PQ$ and $PR$ are the required pair of tangents.

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