Two chords AB and CD of lengths 24 cm and 10 cm respectively of a circle are parallel. If the chords lie on the same side of the centre and distance between them is 7 cm, find the length of a diameter of the circle.
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Question

Two chords AB and CD of lengths 24 cm and 10 cm respectively of a circle are parallel. If the chords lie on the same side of the centre and distance between them is 7 cm, find the length of a diameter of the circle.

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KnowledgeBoat · Accepted Answer

Given: AB and CD are two parallel chords of a circle on the same side of the center. AB = 24 cm and CD = 10 cm. Distance between the chords = MN = 7 cm. Let the radius of the circle be r. Let the perpendicular distance from the center O to chord AB be OM = x. Therefore, ON = x + 7. To Prove: The length of the diameter of the circle. Construction: Join OA and OC. Proof: AM = AB = x 24 = 12 cm In Δ OAM, ∠M = 90° Using Pythagoras theorem, ∴ OA2 = OM2 + AM2 ⇒ r2 = x2 + 122 ⇒ r2 = x2 + 144 ..................(1) CN = CD = x 10 = 5 cm In Δ OCN, ∠N = 90° Using Pythagoras theorem, ∴ OC2 = ON2 + CN2 ⇒ r2 = (x + 7)2 + 52 ⇒ r2 = x2 + 49 + 14x + 25 ⇒ r2 = x2 + 14x + 74 Using equation (1), we get ⇒ x2 + 144 = x2 + 14x + 74 ⇒ 144 = 14x + 74 ⇒ 14x = 144 - 74 ⇒ 14x = 70 ⇒ x = ⇒ x = 5 Putting the value of x in equation (1), we get ⇒ r2 = (5)2 + 144 ⇒ r2 = 25 + 144 ⇒ r2 = 169 ⇒ r = ⇒ r = 13 Diameter = 2r = 2 x 13 cm = 26 cm Hence, the diameter of the circle = 26cm.

Mathematics

Two chords AB and CD of lengths 24 cm and 10 cm respectively of a circle are parallel. If the chords lie on the same side of the centre and distance between them is 7 cm, find the length of a diameter of the circle.

Circles

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Mathematics

Two chords AB and CD of lengths 24 cm and 10 cm respectively of a circle are parallel. If the chords lie on the same side of the centre and distance between them is 7 cm, find the length of a diameter of the circle.

Circles

Related Questions

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(i) ∠AOB
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