find the length of a chord ,5cm away from the center of a circle a radius 13 cm
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Explanation:
answered Mar 9, 2019 by aditya23 (-2,145 points)
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.