In the given figure, MP is tangent to a circle with center A and NQ is a tangent to a circle with center B. If MP = 15 cm, NQ = 8 cm, PA = 17 cm and BQ = 10 cm, then AB is:

14 cm

In right angled triangle PMA

\( { AP}^{2 } \) = \( { PM}^{2 } \) + \( { AM}^{2 } \)

= \( { 17}^{2 } \) = \( { 15}^{2 } \) + \( { AM}^{2 } \)

= \( { AM}^{2 } \) = 289 - 225

= AM = \(\sqrt {64 }\) = 8

In right angled triangle BNQ

\( { BQ}^{2 } \) = \( { BN}^{2 } \) + \( { NQ}^{2 } \)

= \( { 10}^{2 } \) = \( { BN}^{2 } \) + \( { 8}^{2 } \)

= \( { BN}^{2 } \) = 100 - 64

= BN = \(\sqrt {36 }\) = 6

As we know,

AM = AC = 8 and BN = BC = 6 cm.

Now, AB = AC + BC

= AB = 8 + 6 = 14.