In the figure PA and PB are two tangents drawn from an external point P to a circle with center C of radius 4 cm. If PA⊥PB then the length of each tangent is:

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3 cm

4 cm

5 cm

6 cm

answer is B.

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Detailed Solution

The correct answer is 4cm.
Radius of circle= 4cm
Using the figure,

⇒ C A = C B = 4 c m

The tangents drawn to the circle from the external point are equal:

⇒ P A = P B

Given:

P A ⊥ P B

Now, the radius of the circle is perpendicular to the tangent.
We get:

C A ⊥ P A

and

C B ⊥ P B

The quadrilateral CAPB is a square as all angles are 90 degrees and adjacent sides are equal.

⇒ C A = C B = P A = P B = 4 c m

Therefore, the length of tangent is 4cm.
The answer is option 2.

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