Question

In the given fgure, AB is a chord of the outer circle and tangent to the inner circle. If the circkes are concentric
and their radii are 13 cm and 5 cm, then find the length of the chord AB.​

Answer 1

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,

OA²=OM²+AM²

=> 5²=OM²+4²

=> OM=3

=> Hence radius of smaller circle =3cm

so done!