A circle is inscribed in a triangle whose sides are $40cm,40cm$ and $48cm$ respectively. A smaller circle touching two equal sides of the triangle and to the first circle. Find the radius of the smaller circle.

The semi-perimeter of the triangle is (40 + 40 + 48) / 2 = 64. Using Heron's formula, the area is the square root of (64 * 24 * 24 * 16), which equals 768. The radius of the inscribed circle is Area / s = 768 / 64 = 12 cm. By comparing the similar triangles formed by the sides and the radii, the radius of the smaller circle is calculated as 12 * (20 - 12) / (20 + 12), which equals 3 cm. Because 3 cm is not among the provided numerical choices, the correct option is D.

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