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:
Answer & explanation
Correct answer: option 2
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.