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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Answer
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
⇒ OS2 = OT2 + ST2
⇒ 52 = 32 + ST2
⇒ ST2 = 25 - 9
⇒ ST2 = 16
⇒ ST =
⇒ ST = 4 cm.
Similarly, in right triangle OQT, we have
⇒ OQ2 = OT2 + QT2
⇒ 52 = 32 + QT2
⇒ QT2 = 25 - 9
⇒ QT2 = 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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