MathDB
Perpendicular lines

Source: 2020 Latvia TST Round 1

March 30, 2020
geometrycircumcircleparallelogram

Problem Statement

It is given isosceles triangle ABCABC with AB=ACAB = AC. ADAD is diameter of circumcircle of triangle ABCABC. On the side BCBC is chosen point EE. On the sides AC,ABAC, AB there are points F,GF, G respectively such that AFEGAFEG is parallelogram. Prove that DEDE is perpendicular to FGFG.
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