Question

The sum of the radii of two circles is 140 cm and the difference of their circumferences is 88 cm. Find the diameters of the circles.

Answer 1

Let radius of first circle = r₁ cm 

Let radius of second circle = r₂cm 

So, 

r₁ + r₂ = 140 cm …. (i) 

2πr₁ – 2πr₂ = 88 cm 

r₁ - r₂ = \(\frac{88\times7}{2\times22}\) = 14 cm

r₁ - r₂ = 14 cm …. (ii) 

By adding equation 1 & 2 

r₁ = 77 cm 

From equation 1 

77 + r₁ = 140 cm 

r₂ = 140 – 77 = 63 cm 

r₂ = 63 cm 

So, 

Diameter of first circle = 2 × r₁ = 2 × 77 = 154 cm 

Diameter of second circle = 2 × r₂ = 2 × 63 = 126 cm