In the given figure, O is the centre of two concentric circles of radii 5 cm and 3 cm. From an external point P, tangents PA and PB are drawn to these circles. If PA=12 cm, then which of the following is the length of PB?

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52 cm

35 cm

410 cm

510 cm

answer is C.

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Detailed Solution

Consider the given figure,
Question Image

Given that,

O A = 5 c m, P A = 12 cm

, and

O B = 3 cm

.
We know that tangents drawn from an external point are perpendicular to the radius at the point of contact.
Therefore,

∠ O A P = 90 °

.
Applying Pythagoras theorem in

Δ O A P

Applying Pythagoras theorem in ∆OBP.
Question Image

Hence the length of PB is

410 c m

Therefore, option 3 is correct.

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