The figure above shows Line \(L,\) Circle \(1\) with center at \(C_1,\) and Circle \(2\) with center at \(C_2.\) Line

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The figure above shows Line \(L,\) Circle \(1\) with center at \(C_1,\) and Circle \(2\) with center at \(C_2.\) Line \(L\) intersects Circle \(1\) at points \(A\) and \(B,\) Line \(L\) intersects Circle \(2\) at points \(D\) and \(E,\) and points \(C_1\) and \(C_2\) are equidistant from line \(L.\) Is the area of \(\triangle ABC_1\) less than the area of \(\triangle DEC_2?\)

(1) The radius of Circle \(1\) is less than the radius of Circle \(2.\)
(2) The length of chord \(AB\) is less than the length of chord \(DE.\)

Answer: D

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