The figure shows a quadrilateral \( ABCD \) inscribed in a circle. \( \overline{AC} \) is a diameter, \( \overline{AB} = 40 \, cm \) and \( \overline{BC} = 30 \, cm \). What is the area of the shaded region?
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\( 1250 \pi - 600 \) \( cm^2 \)
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\( 2500 \pi \) \( cm^2 \)
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\( 1250 \pi \) \( cm^2 \)
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\( 1200 \pi \) \( cm^2 \)
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Unsufficient data
Try to solve it before checking the answer.
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Unsufficient data
Indeed, the area of the two circular segments can be easily calculated, since it is the area of the semicircle minus the area of the triangle \( \triangle ABC \). However, the area of the shaded triangle \( \triangle ADC \) cannot be calculated, since the height is unknown and the data provided is insufficient to obtain it.