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A Line through the Center That Bisects the Chord Is Perpendicular to the Chord.

Two chords AB...

Question

Two chords AB and CD of a circle intersect each other at P outside the circle. If AB = 6 cm, BP = 2 cm and PD = 2.5 cm, find CD.

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Solution

ANSWER:
AB and CD are two chords of a circle which intersect each other at P outside the circle.
AB = 6 cm, BP = 2 cm and PD = 2.5 cm
∴ AP × BP = CP × DP
⇒ 8 × 2 = (CD + 2.5) × 2.5 [∵ CP = CD + DP ]
Let CD = x cm
Thus, 8 × 2 = (CD + 2.5) × 2.5
⇒ 16 = 2.5 x + 6.25
⇒ 2.5x = (16 - 6.25) = 9.75
⇒ x=9.752.5=3.9
Hence, CD = 3.9 cm

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A Line through the Center That Bisects the Chord Is Perpendicular to the Chord.

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