Question

in two concentric circle the radius of the inner circle is 5 M a chord of length 24 M the outer circle becomes a tangent to the inner circle find the radius of the larger circle

Answer 1

Answer:

13 cm

Step-by-step explanation:

Let O be the centre of concentric circles and AB be the chord of larger circle.

Since,OC is the radius at the point of contact C.

OC ⊥ AB.

Since, AB is the chord of larger circle and OC ⊥ AB.

AC = CB = (1/2)AB.

In ΔOCB,

OB² = OC² + BC²

       = (5)² + [(1/2) * AB]²

       = 5² + [1/2 * 24]²

       = 5² + 12²

       = 169 cm

∴ OB = 13 cm.

Therefore, radius of larger circle = 13 cm.

Hope it helps!

Answer 2

Step-by-step explanation:

chord of big circle is the tangent of the smaller one .

radius of small circle is 5 cm

so the length of the tangent is half at the point at which it touches the small circle

so it is 12 cm

now by Pythagoras theorem we can say

(radius of big circle )square= (5)square +(12)square

which is, (radius)square=25+144

which is, radius= 13 cm