Question

in two concentric circles a chord of length 24cm of larger circle becomes a tangent to the smaller circles whose radius is 5cm.find the
radius of larger circle.

Answer 1

Radius if smaller circle is 5
Chord length of larger circle is 24
if we draw the radius of smaller circle to the tangent it is dvided into half
so each part become 12
By Pythagoras theorem te radius of larger circle is 13

Answer 2

Length of chord of larger circle = 24cm

radius of smaller circle = 5cm

So by joining the centre and point of tangent of smaller circle we get a radius of smaller circle of 5cm.

And which is perpendicular to tangent and so as it is chord so it will get bisected by radius

Now,

join one end of chord with the centre and that forms a right-angled triangle,

Now let's find the radius of larger circle by using pythagoras theorem.


let radius of larger circle be OA = ?
let radius of smaller circle be OL = 5cm
and Chord be AB = 24cm

So,
AL=12cm

OA^2= OL^2+AL^2

OA^2=25+144

OA^2=169

we get,

OA = 13cm

radius of larger circle is 13cm