question_answer

If PT is a tangent and AB is a chord of a circle and they intersect at the point P externally and PT= 2 AP and AB = 18 units, then PT equals to

A) 6 units

B) 9 units

C) 12 units

D) 15 units

Correct Answer: C

Solution :

[c] From figure,                         \[P{{T}^{2}}=PA\cdot PB\]             \[\Rightarrow \]   \[{{(2x)}^{2}}=x\,(18+x)\] \[\Rightarrow \]   \[4{{x}^{2}}=x\,(18+x)\] \[\Rightarrow \]   \[4x=18+x\]\[\Rightarrow \]\[x=6\] \[\therefore \]      \[PT=2\times 6=12\,\text{units}\]