Question
Download Solution PDFTwo chords of a circle, \(\rm \overline{AB}\) and \(\rm \overline{CD}\), meet outside the circle at the point P. If m(\(\rm \overline{AP}\)) = 200 mm, m(\(\rm \overline{AB}\)) = 120 mm, and m(\(\rm \overline{CP}\)) = 160 mm, what is the length of \(\rm \overline{CD}\)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven :
m(\(\rm \overline{AP}\)) = 200 mm, m(\(\rm \overline{AB}\)) = 120 mm, and m(\(\rm \overline{CP}\)) = 160 mm
Calculation :
Let the length of CD be x.
⇒ AP × BP = CP × DP
⇒ 200 × 80 = 160 × (160 -x)
⇒ 16000 = 160 × (160 -x)
⇒ 16000 = 25600 - 160x
⇒ x = 9600/160
⇒ x = 60 mm
∴ The correct answer is 60 mm.
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