In a circle with
center 0 & radius
13 cm a chord
АВ. is drawn at a
distance of 5 cm
from the center
of a circler than
find the lenth of
chord
AB
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Let AB be a chord of a circle with centre O and radius 13 cm. Draw OL ⊥ AB.
Join OA. Clearly, OL = 5 cm and OA = 13 cm.
In the right triangle OLA, we have
OA2 = OL2 + AL2
⇒ 132 = 52 + AL2
⇒ AL2 = 144 cm2
⇒ AL = 12 cm
Since, the perpendicular from the centre to the chord bisects the chord. Therefore,
AB = 2AL = (2 × 12) cm
= 24 cm.
Let AB be a chord of a circle with centre O and radius 13 cm. Draw OL ⊥ AB.
Join OA. Clearly, OL = 5 cm and OA = 13 cm.
In the right triangle OLA, we have
OA2 = OL2 + AL2
⇒ 132 = 52 + AL2
⇒ AL2 = 144 cm2
⇒ AL = 12 cm
Since, the perpendicular from the centre to the chord bisects the chord. Therefore,
AB = 2AL = (2 × 12) cm
= 24 cm.
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