A circle of radius 2.5 cm has a chord of length 4.8 cm. Find the distance of the chord from the centre of the circle.
Circles
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Question

A circle of radius 2.5 cm has a chord of length 4.8 cm. Find the distance of the chord from the centre of the circle.

KnowledgeBoat · Accepted Answer

From figure, Given: Length of the chord AC = 4.8 cm. Radius of the circle (r) = 2.5 cm Distance of the chord from the center of the circle = OB. B is the midpoint of AC, as OB is perpendicular to the chord AC. AB = AC = = 2.4 cm. In Δ OAB, ∠B = 90° Using Pythagoras theorem, ∴ OA2 = OB2 + AB2 ⇒ (2.5)2 = OB2 + (2.4)2 ⇒ 6.25 = OB2 + 5.76 ⇒ OB2 = 6.25 - 5.76 ⇒ OB2 = 0.49 ⇒ OB = ⇒ OB = 0.7 cm. Hence, the distance of the chord from the center of the circle is 0.7 cm.

Mathematics

A circle of radius 2.5 cm has a chord of length 4.8 cm. Find the distance of the chord from the centre of the circle.

Circles

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