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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.

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Answer

We know that,

The tangent at any point of a circle and the radius through this point are perpendicular to each other.

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. Tangents and Intersecting Chords, Concise Mathematics Solutions ICSE Class 10.

In right triangle OST, we have

⇒ OS2 = OT2 + ST2

⇒ 52 = 32 + ST2

⇒ ST2 = 25 - 9

⇒ ST2 = 16

⇒ ST = 16\sqrt{16}

⇒ ST = 4 cm.

Similarly, in right triangle OQT, we have

⇒ OQ2 = OT2 + QT2

⇒ 52 = 32 + QT2

⇒ QT2 = 25 - 9

⇒ QT2 = 16

⇒ QT = 16\sqrt{16}

⇒ 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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