A chord of length 16 cm is at a distance 6 cm from the center of the circle. Find the length of chord of the same circle which is at a distance of 8 cm from the center.
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Question

A chord of length 16 cm is at a distance 6 cm from the center of the circle. Find the length of chord of the same circle which is at a distance of 8 cm from the center.

KnowledgeBoat · Accepted Answer

From figure, AB is the chord which is at a distance 6 cm from the center so OC = 6 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 = 6² + 8² ⇒ OA² = 36 + 64 ⇒ OA² = 100 ⇒ OA = = 10 cm. Radius = 10 cm, ∴ OD = 10 cm. From figure, In right angle triangle ODF, ⇒ OD² = OF² + DF² (By pythagoras theorem) ⇒ DF² = OD² - OF² ⇒ DF² = 10² - 8² ⇒ DF² = 100 - 64 = 36 ⇒ DF = = 6 cm. Since, the perpendicular to a chord from the centre of the circle bisects the chord ∴ DE = DF + FE = 6 cm + 6 cm = 12 cm. Hence, the length of chord which is at a distance of 8 cm from the center of the circle = 12 cm.

Mathematics

A chord of length 16 cm is at a distance 6 cm from the center of the circle. Find the length of chord of the same circle which is at a distance of 8 cm from the center.

Circles

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Mathematics

A chord of length 16 cm is at a distance 6 cm from the center of the circle. Find the length of chord of the same circle which is at a distance of 8 cm from the center.

Circles

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