The radius of a circle is 40 cm and the length of perpendicular drawn from its centre to chord is 24 cm. Find the length of chord.
Circles
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Question

The radius of a circle is 40 cm and the length of perpendicular drawn from its centre to chord is 24 cm. Find the length of chord.

KnowledgeBoat · Accepted Answer

From figure, Given: Radius of the circle (r) = 40 cm AC is the chord and OB is the perpendicular distance from center. B is the midpoint of AC, as OB is perpendicular to the chord AC. AB = AC In Δ OAB, ∠B = 90° Using Pythagoras theorem, ∴ OA2 = OB2 + AB2 ⇒ (40)2 = (24)2 + AB2 ⇒ 1600 = 576 + AB2 ⇒ AB2 = 1600 - 576 ⇒ AB2 = 1024 ⇒ AB = ⇒ AB = 32 cm Length of the chord = AC = 2(AB) = 2(32) = 64 cm. Hence, the length of the chord is 64 cm.

Mathematics

The radius of a circle is 40 cm and the length of perpendicular drawn from its centre to chord is 24 cm. Find the length of chord.

Circles

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