In the figure, common tangents \( P Q \) and \( R S \) to two circles intersect at \( A \). Prove that \( P Q=R S \).

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Given:

In the figure, common tangents \( P Q \) and \( R S \) to two circles intersect at \( A \).

To do:

We have to prove that \( P Q=R S \).

Solution:

$AQ$ and $AR$ are two tangents drawn from $A$ to the circle with centre $O$.

$AP = AR$....….(i)

Similarly,

$AQ$ and $AS$ are the tangents to the circle with centre $C$.

$AQ = AS$....….(ii)

Adding (i) and (ii), we get,

$AP + AQ = AR + AS$

$PQ = RS$

Hence proved.

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Updated on: 10-Oct-2022

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