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angle wanted, midpoints, perpendiculars (2018 Kyiv City MO 7.4.1)

Source:

September 11, 2020
geometryanglesmidpointsperpendicular

Problem Statement

In the quadrilateral ABCDABCD point EE - the midpoint of the side ABAB, point FF - the midpoint of the side BCBC, point GG - the midpoint ADAD . It turned out that the segment GEGE is perpendicular to ABAB, and the segment GFGF is perpendicular to the segment BCBC. Find the value of the angle GCDGCD, if it is known that ∠ADC=70∘\angle ADC = 70 {} ^ \circ.
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