A Tricky Trapezoid

Geometry Level 3

In the diagram below, trapezoid \(ABCD\) has \( AB \parallel CD\). \(\overline{AB} = 24, \overline{CD} = 14, \angle ADC = 156,\) and \( \angle DCB = 114 \) (angles are in degrees). Find the distance between the midpoints of \(AB\) and \(CD\).

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