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PAB is a tangent which is common to two circles which touches each other at point X. The tangent touches the smaller circle at A and larger circle at B. If PA = 20 cm and the radius of smaller circle is 15 cm, then find the radius of larger circle.

PAB is a tangent which is common to two circles which touches each other at point X. The tangent touches the smaller circle at A and larger circle at B. If PA = 20 cm and the radius of smaller circle is 15 cm, then find the radius of larger circle. Correct Answer 60 cm

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M and N are the centres of smaller and larger circle respectively.

In ΔPMA:

PM2 = 400 + 225 = 625

⇒ PM = 25 cm

Suppose NB = NX = R cm

We can observe that ΔPMA and ΔPNB are similar triangles

∴ PM/PN = AM/BN

⇒ PM/(PM + MX + XN) = AM/NB

⇒ 25/(25 + 15 + R) = 15/R

⇒ 25/(40 + R) = 15/R

⇒ 5R = 3R + 120

⇒ 2R = 120

⇒ R = 60

∴ Radius of larger circle = 60 cm

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