In the figure, chords AB and CD of a circle intersect externally at P. If AB = 4 cm, CD = 11 cm, and PD = 15 cm, then the length of PB is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 10 cm
PD = 15 cm then PC = 15 - 11 = 4 cm
Let PA = x cm.
By using tangent secant theorem we get,
PA × PB = PC × PD
x (x + 4) = 4 × 15
By hit and trial,
6(6 + 4 ) = 60
60 = 60
So x = 6.
PB = x + 4 = 6 + 4 = 10 cm.