Question

Two concentric circles are of radii 7 cm and r cm respectively , where r >7 . A chord of the larger circle , of length 48 cm, touches the smaller circle . Find the value of r.

Answer 1

Answer:

The radius will be 25 cm.

Let's see how?

Step-by-step explanation:

We have to find the radius of the circle i.e. R.

Now using pythagoras theorem: -

(Hypotenues)^2 = (Perpendicular)^2  +  (Base)^2    

(R)^2 = (24)^2 + (7)^2

(R)^2 = (576) + (49)

(R)^2 = 625

(Square rooting both sides)

=>   R = √625

         =25

∴ The radius of the circle is equal to 25 cm.

Answer 2

Given: Two concentric circles are of radii 7 cm and r cm respectively , where r >7 . A chord of the larger circle , of length 48 cm, touches the smaller circle.

To find: The value of r.

Solution: The value of r is 25 cm.

The perpendicular from the centre of the smaller circle to the chord forms the perpendicular of a right-angled triangle. This perpendicular is equal to the radius of the smaller circle.

The point where the chord touches the smaller circle to the point where the chord touches the circumference of the larger circle forms the base. Since the length of the base is half the length of the chord, it can be calculated as shown below.

$\frac{48}{2} = 24 cm$

The hypotenuse of this right-angled triangle becomes the radius of the larger circle (r).

$r = \sqrt{(24)^{2} + (7)^{2} }$

   $= 25 cm$

Therefore, the value of r is 25 cm.