In the following figure, if PT= 12 cm and PB= 24 cm, then find AB.

24 cm 18 cm 16 cm 12 cm

18 cm

Formula Used From the tangent theorem, \( {PT }^{2 } \) = PA x PB Calculations = Here, PT = 12 cm = PB = 24 cm Now, put the value of PT and PB = \( {PT }^{2 } \) = PA x PB = \( {12 }^{2 } \) = PA x 24 = PA = \(\frac{144}{24}\) = 6 cm As we know, = PB = PA + AB = AB = PB - PA = 24 - 6 = 18 cm Therefore, AB is 18 cm.