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$PA$ and $PB$ are two tangents drawn touching a circle with centre C. If the radius is $4$ cm and $P A ⊥ PB$ , then the length of each tangent will be

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3cm

4cm

5cm

6cm

answer is B.

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Detailed Solution

Given that the radius of the circle is

4

cm and

P A ⊥ PB

.
We join

CA

and

CB

Let R be the radius and T be the Tangent.
We know that R and T are perpendicular at their point of contact,

∴ ∠ C A P = ∠ C B P = 90 °

In quadrilateral

ACBP

all the angles are right angles.
Therefore,

ACBP

is a rectangle,
In a rectangle, we know that the opposite sides are equal.

∴ CB = AP

and

CA = BP

⇒ C B = A P = 4 cm

⇒ C A = B P = 4 cm

Thus, the length of each tangent will be

4

cm.
Therefore the correct option will be 2.

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