Mathematics
There are two concentric circles, each with centre O and of radii 10 cm and 26 cm respectively. Find the length of the chord AB of the outer circle which touches the inner circle at P.
Circles
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Answer
AB is the chord of the outer circle which touches the inner circle at P.
OP is the radius of the inner circle and APB is the tangent to the inner circle.
In the right angled triangle OPB, by pythagoras theorem,
⇒ OB2 = OP2 + PB2
⇒ 262 = 102 + PB2
⇒ 676 = 100 + PB2
⇒ PB2 = 676 - 100
⇒ PB2 = 576
⇒ PB =
⇒ PB = 24 cm
As perpendicular line from centre bisects the chord of the circle so,
AP = PB = 24 cm.
AB = AP + PB = 24 + 24 = 48 cm.
Hence, the length of chord (AB) = 48 cm.
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