Question

out of 2 concentric circkes , the radius of outer circkeis 5cm and the chord AC of length 8 cm is a tangent to the inner circle . find r

Answer 1

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Answer 2

Correct option is

A

3cm

According to question,

Radius of larger circle is 5cm

and length of tangent AC to smaller circle is 8cm.

We know that , tangent is perpendicular to radius through point of tangency,

And M, is the mid point of tangent from figure,

so AM=4cm

Therefore ,

△AMO is the right angle triangle, with OM as radius of smaller circle,

So, from pythagorous theorem,

$OA </p><p>2</p><p> =OM </p><p>2</p><p> +AM </p><p>2</p><p> </p><p></p><p>=> 5 </p><p>2</p><p> =OM </p><p>2</p><p> +4 </p><p>2</p><p></p><p>$

=> OM=3

=> Hence radius of smaller circle =3cm

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