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P is a point on the diameter AB of a circle and CD is a chord perpendicular to AB. If AP = 4 cm and PB = 16 cm, the length of chord CD is



  • a)
    16 cm

  • b)
    20 cm

  • c)
    10 cm

  • d)
    8 cm

Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
P is a point on the diameter AB of a circle and CD is a chord perpendi...
Join OC
and now AB = AP+ PB = 20
therefore radius= 10 cm
hence OC = 10 = OA ( radius of circle)
Now AP = 4
hence = PO = OA - AP
= 10-4
Therefore PO = 6
by Pythagoras theorem

(OC)² = (PC)²+(PO)²
(PC)² = (OC)²- (PO)²
=100 - 36
(PC)²= 64
PC = √64
PC = 8
now 2PC = 16
Chord CD = 16 cm।।।। Answer।।।।
Free Test
Community Answer
P is a point on the diameter AB of a circle and CD is a chord perpendi...
AP+PB=AB [diameter of circle]
4+16=20[diameter]
so r=AO = CO=10
so clearly PO= OA-AP=10-4=6
PO=6 OC=10 So just apply pythagoreus theorem in triangle PCO
so CP will come 8 So chord CD = 2x8 = 16
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P is a point on the diameter AB of a circle and CD is a chord perpendicular to AB. If AP = 4 cm and PB = 16 cm, the length of chord CD isa)16 cmb)20 cmc)10 cmd)8 cmCorrect answer is option 'A'. Can you explain this answer?
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