A chord of length 16 cm is drawn in a circle of radius 10 cm. Calculate the distance of the chord from the centre of the circle.
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Question

A chord of length 16 cm is drawn in a circle of radius 10 cm. Calculate the distance of the chord from the centre of the circle.

KnowledgeBoat · Accepted Answer

Given: Length of the chord AC = 16 cm. Radius of the circle (r) = 10 cm Diameter of the circle = 10 x 2 = 20 cm. Draw OB ⊥ AC, where O is the center of the circle. Join OA. B is the midpoint of AC, as OB is perpendicular to the chord AC. AB = AC = = 8 cm. In Δ OAB, ∠B = 90° Using Pythagoras theorem, ∴ OA2 = OB2 + AB2 ⇒ (10)2 = OB2 + (8)2 ⇒ 100 = OB2 + 64 ⇒ OB2 = 100 - 64 ⇒ OB2 = 36 ⇒ OB = ⇒ OB = 6 cm. Hence, the distance of the chord from the center of the circle is 6 cm.

Mathematics

A chord of length 16 cm is drawn in a circle of radius 10 cm. Calculate the distance of the chord from the centre of the circle.

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