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:

MP is tangent to the circle with center A. So MP is perpendicular to AM.

From $$\triangle\ $$PAM,

AM$$^2$$ + MP$$^2$$ = PA$$^2$$

$$\Rightarrow$$  AM$$^2$$ + 15$$^2$$ = 17$$^2$$

$$\Rightarrow$$  AM$$^2$$ + 225 = 289

$$\Rightarrow$$  AM$$^2$$ = 64

$$\Rightarrow$$  AM = 8 cm

Radius of larger circle = AC = AM = 8 cm

NQ is tangent to the circle with center B. So NQ is perpendicular to BN.

From $$\triangle\ $$QBN,

BN$$^2$$ + NQ$$^2$$ = BQ$$^2$$

$$\Rightarrow$$  BN$$^2$$ + 8$$^2$$ = 10$$^2$$

$$\Rightarrow$$  BN$$^2$$ + 64 = 100

$$\Rightarrow$$  BN$$^2$$ = 36

$$\Rightarrow$$  BN = 6 cm

Radius of smaller circle = BC = BN = 6 cm

$$\therefore\ $$AB = AC + BC = 8 + 6 = 14 cm