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Class 8-9-10, JEE & NEET
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Two concentric circles are of radii 6.5 cm and 2.5 cm. Find the length of the chord of the larger circle which touches the smaller circle
We know that the radius and tangent are perperpendular at their point of contact
In right triangle AOP
AO = OP + PA
⇒ (6.5) = (2.5) + PA
⇒ PA = 36
⇒ PA = 6 cm
Since, the perpendicular drawn from the centre bisect the chord.
∴ PA = PB = 6 cm
Now, AB = AP + PB = 6 + 6 = 12 cm
Hence, the length of the chord of the larger circle is 12 cm.