# 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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