Mathematics
Chords AB and CD of a circle when extended meet at point X. Given AB = 4 cm, BX = 6 cm and XD = 5 cm, calculate the length of CD.
Circles
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Answer
Chords AB and CD of the circle meeting at point X are shown below:
We know that,
If two chords of a circle intersect internally or externally then the product of the lengths of their segments is equal.
⇒ XB.XA = XD.XC
⇒ 6.(6 + 4) = 5.(5 + CD)
⇒ 6 × 10 = 25 + 5CD
⇒ 5CD = 60 - 25
⇒ 5CD = 35
⇒ CD =
⇒ CD = 7 cm.
Hence, CD = 7 cm.
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