In the given figure, the circles are concentric and AB is the tangent to the smaller circle. If the length of RB is 3 cm, find the length of AB.

3 cm

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6 cm

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9 cm

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4 cm

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Solution

The correct option is B 6 cm

For the larger circle, if a line from the centre of the circle is perpendicular to the chord, it bisects the chord.

For the smaller circle, the radius of the circle at the point of contact of the tangent to the circle is perpendicular to the circle.

Using the above two, we can say that R is the mid-point of AB.
Hence, AR = RB = 3 cm
and AB = 2AR = 2RB = $2 \times 3 = 6$ cm

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