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Standard X

Mathematics

Length of Tangents Drawn from an External Point

In the given ...

Question

In the given figure, PA and PB are tangents drawn from an external point P to a circle. CD is the third tangent touching the circle at Q. If PB=10cm and CQ=2cm, then the length of PC is:

14 cm

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8 cm

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10 cm

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12 cm

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Solution

The correct option is
C

8 cm
Given: PA and PB are the tangents to the circle.
$P B = 10 c m$ , $C Q = 2 c m$
We know that the lengths of the tangents drawn from an external point are equal.

$P B = P A = 10 c m$
Similarly $C Q = C A = 2 c m$

Now, $P C = P A - C A = 10 c m - 2 c m = 8 c m$

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In the given figure, PA and PB are tangents drawn from an external point P to a circle. CD is the third tangent touching the circle at Q. If PB=10cm and CQ=2cm, then the length of PC is:

The correct option is C 8 cmGiven: PA and PB are the tangents to the circle.PB=10 cm, CQ=2 cmWe know that the lengths of the tangents drawn from an external point are equal. PB=PA=10 cm Similarly CQ=CA=2 cm Now, PC=PA−CA=10 cm−2 cm=8 cm

The correct option is
C

8 cm
Given: PA and PB are the tangents to the circle.
$P B = 10 c m$ , $C Q = 2 c m$
We know that the lengths of the tangents drawn from an external point are equal.

$P B = P A = 10 c m$
Similarly $C Q = C A = 2 c m$

Now, $P C = P A - C A = 10 c m - 2 c m = 8 c m$