Chords AB and CD of a circle, when produced, meet at the point P. If AB = 6.3 cm, BP = 4.5 cm, and CD = 3.6 cm then the length ( in cm) of PD is
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Correct answer: D
Explanation
The correct answer is option 4 i.e. 5.4 cm
let AP = AB + BP = 6.3 + 4.5 = 10.8 cm
( let PD = x )
CP = CD + PD = 3.6 + x
now AP × PB =CP × PD
⇒ 10.8 × 4.5 =( 3.6 + x ) × x
48.6 = x2 + 3.6x
⇒ x2 + 3.6x - 48.6 = 0
⇒ x2 + 9x - 5.4x - 48.6 = 0
⇒ x(x + 9) - 5.4(x + 9) = 0
⇒ (x + 9) (x - 5.4) = 0
x = -9, 5.4
PD = x = 5.4 cm