in a circle of radius 10cm find the length of a chord which is at a distance of 5cm from its center.
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Let a circle with center O of radius OA = 10 cm.
and length of chord = AB = AM + MB
and OM divides the into two equal parts.
i.e, AM = MB
therefore AB = 2.AM
given,
distance between center and chord = OM = 5 cm.
from ΔOMA
(OA) ² = (AM)² + (OM)²
⇒ 10² = (AM)² + 5²
⇒ 100 = (AM)² + 25
⇒ (AM)² = 100 - 25 = 75
∴ AM = √75 = 5√3 cm
Therefore length of chord) = AB = 2.AM = 2×5√3 =10√3 cm
and length of chord = AB = AM + MB
and OM divides the into two equal parts.
i.e, AM = MB
therefore AB = 2.AM
given,
distance between center and chord = OM = 5 cm.
from ΔOMA
(OA) ² = (AM)² + (OM)²
⇒ 10² = (AM)² + 5²
⇒ 100 = (AM)² + 25
⇒ (AM)² = 100 - 25 = 75
∴ AM = √75 = 5√3 cm
Therefore length of chord) = AB = 2.AM = 2×5√3 =10√3 cm
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mmithastudent:
thanku your answer is correct.
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