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In the figure chords AB and CD of a circle intersect...

This question belongs to Arithmetic Ability Geometry
Geometry
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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:
Geometry mcq question image

Answer & Solution
Correct Answer: Option A
Let, PA = x
PA × PB = PC × PD
x × (x + 4) = 4 × 15
x × (x + 4) = 60
x2 + 4x - 60 = 0
x2 + 10x - 6x - 60 = 0
x(x + 10) - 6(x + 10) = 0
x = 6
PB = x + 4 = 6 + 4 = 10 cm
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