Two concentric circlles are of radii (3x + 5) and (2x - 4) cm (x > 0). Length of the chord of the outer circle which touches the inner circle 48 cm. Find the radii of the two circles.

Let the radius of the bigger circle be (3x + 5) and radius of the smaller circle is (2x - 4)

Since the perpendicular from the centre to the chord bisects the chord.

So apply Pythagoras theorem in order to get,

So radius of bigger circle = 3(7) +5 = 26 units

Radius of smaller circle = 2(7) - 4 = 10 units

• 1

I thnk its 2root5 i.e., 4.4 cm

3x+5 will be the radius of the bigger circle and 2x-4 of the smaller circle.

This implies 3x

• -2

Oopsie i am sry it got posted by mistake half way thru!

• -3
I am nt very sure, so pls correct me if i am wrong
I thnk its 2root5 i.e., 4.4 cm
3x+5 will be the radius of the bigger circle and 2x-4 of the smaller circle.
This implies (3x+5)^2=(2x-4)^2+24^2
9x^2+25+30x=4x^2+16-16x+576
5x^2+46x-567=0
5x^2+46x+526=567+526       (Completing the square method)
(root(5)x+23)^2=1093
root(5)x+23=+/-33    (approx.)
x=(+/-33-23)root(5)/5  (after rationalising the denominator)
which gives 10root(5)/5 or -56root(5)/5
Bt since sides of a triangle cannot be negative,