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

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

Source: Official Guide

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