Question 200

Two circles touch each other externally. The sum of their areas is 130 $$\pi$$ sq cm and the distance between their centres is 14 cm. The radius of the smaller circle is

Solution

Let the radius of bigger circle = $$x$$ and smaller circle = $$y$$

Now, distance between their centres = 14

=> $$x + y$$ = 14

Sum of their areas = 130$$\pi cm^2$$

=> $$\pi x^2 + \pi y^2 = 130\pi$$

=> $$x^2 + y^2 = 130$$

Now, solving above equations, we get $$x = 11$$

and $$y = 3$$

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