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DF= CG wanted, perpendiculars inside a square

Source: Moldova JBMO TST 2016 2.3

July 10, 2020
geometryperpendicularsquareequal segments

Problem Statement

Let ABCDABCD ba a square and let point EE be the midpoint of side ADAD. Points GG and FF are located on the segment (BE)(BE) such that the lines AGAG and CFCF are perpendicular on the line BEBE. Prove that DF=CGDF= CG.
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