Ratio of areas

Geometry Level 2

RS \text{RS} is the diameter of a semicircle shown above. Two smaller semicircles are drawn on RS \text{RS} and their common internal tangent AT \text{AT} intersects the large semicircle at A \text{A} . Find the ratio of the area of the semicircle with radius AT \text{AT} to the area of the shaded region.

2 1.5 \dfrac{2}{1.5} 2 1 \dfrac{2}{1} 5 3 \dfrac{5}{3} 3 2 \dfrac{3}{2}

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