Two circles of radii 17 cm and 25 cm intersect each other at two points A and B. If the length of common chord AB of the circles is 30 cm, find the distance between the centres of the circles.
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Question

Two circles of radii 17 cm and 25 cm intersect each other at two points A and B. If the length of common chord AB of the circles is 30 cm, find the distance between the centres of the circles.

KnowledgeBoat · Accepted Answer

Since, the perpendicular to a chord from the centre of the circle bisects the chord, ∴ AC = CB = = 15 cm From figure, In right triangle OAC, ⇒ OA2 = OC2 + AC2 (By pythagoras theorem) ⇒ 252 = OC2 + 152 ⇒ 625 = OC2 + 225 ⇒ OC2 = 400 ⇒ OC = = 20 cm. In right triangle O'AC, ⇒ O'A2 = O'C2 + AC2 (By pythagoras theorem) ⇒ 172 = O'C2 + 152 ⇒ 289 = O'C2 + 225 ⇒ O'C2 = 64 ⇒ O'C = = 8 cm. Distance between centers = OO' = OC + O'C = 20 + 8 = 28 cm. Hence, distance between their centres = 28 cm.

Mathematics

Two circles of radii 17 cm and 25 cm intersect each other at two points A and B. If the length of common chord AB of the circles is 30 cm, find the distance between the centres of the circles.

Circles

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