A chord of length 8 cm is at a distance 3 cm from the centre of the circle. Calculate the radius of the circle.
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Question

A chord of length 8 cm is at a distance 3 cm from the centre of the circle. Calculate the radius of the circle.

KnowledgeBoat · Accepted Answer

From figure, AB is the chord which is at a distance 3 cm from the center so OC = 3 cm. Since, the perpendicular to a chord from the centre of the circle bisects the chord, ∴ CB = AC = = 4 cm. In right angle triangle OAC, ⇒ OA² = OC² + AC² (By pythagoras theorem) ⇒ OA² = 3² + 4² ⇒ OA² = 9 + 16 ⇒ OA² = 25 ⇒ OA = = 5 cm. Hence, radius = 5 cm.

Mathematics

A chord of length 8 cm is at a distance 3 cm from the centre of the circle. Calculate the radius of the circle.

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