A chord of length 16 cm is at a distance of 15 cm from centre of the circle. Find the length of chord of same circle which is at 8 cm away from circle.
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Question

A chord of length 16 cm is at a distance of 15 cm from centre of the circle. Find the length of chord of same circle which is at 8 cm away from circle.

KnowledgeBoat · Accepted Answer

From figure, AB is the chord of length 16 cm which is at a distance 15 cm from the center so OC = 15 cm. Since, the perpendicular to a chord from the centre of the circle bisects the chord, ∴ CB = AC = = 8 cm In right angle triangle OAC, ⇒ OA2 = OC2 + AC2 (By pythagoras theorem) ⇒ OA2 = 152 + 82 ⇒ OA2 = 225 + 64 ⇒ OA2 = 289 ⇒ OA = ​ ⇒ OA = 17 cm Radius = 17 cm, ∴ OD = 17 cm. From figure, In right angle triangle ODF, ⇒ OD2 = OF2 + DF2 (By pythagoras theorem) ⇒ DF2 = OD2 - OF2 ⇒ DF2 = 172 - 82 ⇒ DF2 = 289 - 64 = 225 ⇒ DF = = 15 cm. Since, the perpendicular to a chord from the centre of the circle bisects the chord. DF = FE = 15 cm From figure, DE = DF + FE = 15 cm + 15 cm = 30 cm. Hence, the length of chord which is at a distance of 8 cm from the center of the circle = 30 cm.

Mathematics

A chord of length 16 cm is at a distance of 15 cm from centre of the circle. Find the length of chord of same circle which is at 8 cm away from circle.

Circles

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