Two circles of radii '$a$' and '$b$' touching each other externally, are inscribed in the area bounded by $y = \sqrt{1 -x^2}$ and the x-axis. If $b = \dfrac{1}{2}$, then a is equal to

The given curve y = sqrt(1 - x^2) is a semicircle of radius 1 centered at the origin. The centers of the inscribed circles of radii a and b will lie on the y-axis at (0, 1-a) and (0, 1-b) respectively. Since the circles touch each other externally, the distance between their centers equals the sum of their radii, giving the equation (1-a) - (1-b) = a + b. Substituting b = 1/2 into the equation yields 1/2 - a = a + 1/2, which means a is 1/4.

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