Mathematics
Two chords AB, CD of a circle intersect externally at a point P. If PB = 7 cm, AB = 9 cm and PD = 6 cm, find CD.
Circles
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Answer
We know that,
If two chords of a circle intersect externally, then the products of the length of segments are equal.
From figure,
PA.PB = PC.PD …..(i)
PA = PB + AB = 7 + 9 = 16 cm.
Putting values in equation (i) we get,
⇒ 16 × 7 = PC × 6
⇒ 112 = PC × 6
⇒ PC =
⇒ PC = .
From figure,
CD = PC - PD =
Hence, the value of CD = cm.
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