Mathematics
Two chords AB and CD of a circle intersect at a point P inside the circle such that AB = 12 cm, AP = 2.4 cm and PD = 7.2 cm. Find CD.
Circles
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Answer
We know that,
If two chords of a circle intersect internally, then the products of the length of segments are equal.
AP × PB = CP × PD
PB = AB - AP = 12 - 2.4 = 9.6 cm
Substituting values we get,
⇒ 2.4 × 9.6 = CP × 7.2
⇒ CP =
⇒ CP = 3.2 cm
⇒ CD = CP + PD = 3.2 + 7.2 = 10.4 cm
Hence, CD = 10.4 cm.
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