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प्रश्न
In two concentric circles, a chord of length 8 cm of the large circle touches the smaller circle. If the radius of the larger circle is 5 cm, then find the radius of the smaller circle.
उत्तर
We know that the radius and tangent are perpendicular at their point of contact since the perpendicular drawn from the centre bisects the chord.
∴ AP = PB = `(AB)/2` = 4 cm
In the right triangle, AOP
AO2 = OP2 + PA2
⇒ 52 = OP2 + 42
⇒ OP2 = 9
⇒ OP = 3 cm
Hence, the radius of the smaller circle is 3 cm.
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