Two circles of radii 5 cm and 3 cm are concentric. Calculate the length of a chord of the outer circle which touches the inner.

We know that, The tangent at any point of a circle and the radius through this point are perpendicular to each other. In right triangle OST, we have ⇒ OS 2 = OT 2 + ST 2 ⇒ 5 2 = 3 2 + ST 2 ⇒ ST 2 = 25 - 9 ⇒ ST 2 = 16 ⇒ ST = ⇒ ST = 4 cm. Similarly, in right triangle OQT, we have ⇒ OQ 2 = OT 2 + QT 2 ⇒ 5 2 = 3 2 + QT 2 ⇒ QT 2 = 25 - 9 ⇒ QT 2 = 16 ⇒ QT = ⇒ QT = 4 cm. From figure, QS = ST + QT = 4 + 4 = 8 cm. Hence, the length of a chord of the outer circle which touches the inner = 8 cm.

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Mathematics

Two circles of radii 5 cm and 3 cm are concentric. Calculate the length of a chord of the outer circle which touches the inner.

Circles

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