Question

6. Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tangent to the inner circle. Find the radius of the inner circle.ex
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Answer 1

Answer:

Correct option is A)

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 ^2 =OM ^2 +AM ^2

5 ^2=OM^ 2+4^ 2

=> OM=3

=> Hence radius of smaller circle =3cm