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Question

In fig., PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4cm. If PA PB, then the length of each tangent is:
494253_bd09b4e3cd3d4cf892041d7cea3f98b0.png

A
3 cm
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B
4 cm
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C
5 cm
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D
6 cm
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Solution

The correct option is A 4 cm
Given that PA and PB are two tangent drawn from an external point P.
And a circle with center C and radius 4 cm and PAPB
Join center C with A and B
Given PA and PB are tangent of circle.
Then PACA and PBCB
Therefore, CAP=900 and CBP=900

But given, APB=900
Therefore, CBA=900

Therefore, quadrilateral ABCD has all angles equal i.e. 900
and adjacent sides equal.
Hence, it is a square.
Therefore, length of each tangent will be 4 cm

554043_494253_ans_c0d05c40811b4ccab067ab2067962996.png

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