Mathematics
Calculate the length of a chord which is at a distance 6 cm from the center of a circle of diameter 20 cm.
Circles
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Answer
Diameter = 20 cm,
∴ Radius = = 10 cm.
From figure,
AB is the chord which is at a distance 6 cm so,
OC = 6 cm and OA = radius = 10 cm.
In right angle triangle OAC,
⇒ OA2 = OC2 + AC2 (By pythagoras theorem)
⇒ 102 = 62 + AC2
⇒ AC2 = 102 - 62
⇒ AC2 = 100 - 36 = 64
⇒ AC = = 8 cm.
Since, the perpendicular to a chord from the centre of the circle bisects the chord,
∴ CB = AC = 8 cm.
AB = AC + CB = 8 + 8 = 16 cm.
Hence, length of chord = 16 cm.
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