Given:

Let the two circles be C₁ and C₂ with diameters 10 cm and 24 cm respectively.

Area of circle, C = Area of C₁ + Area of C₂ …… (i)

∵ Diameter = 2 × radius

∴ Radius of C₁, r₁ = = 5 cm

and Radius of C₂, r₂ = = 12 cm

∵ Area of circle = πr² …… (ii)

∴ Area of C₁ = πr₁²

=

=

= cm²

Similarly, Area of C₂ = πr₂²

=

= 22/7 × 144

= cm²

∴ Using equation (i), we have

Area of C = +

= cm²

Now, using equation (ii), we have

× r² =

r² =

r² = 169

r =

r = 13 cm

⇒ Diameter = 2 × r

= 2 × 13

= 26 cm

Hence, the diameter of the circle is 26 cm.