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Slovenia 2019 TST1 P1

Source: 2019 Slovenia 1st TST P1

February 18, 2019
TSTgeometry

Problem Statement

Let ABCABC be a non-right isosceles triangle such that AC=BCAC = BC. Let DD be such a point on the perpendicular bisector of ABAB, that ADAD is tangent on the ABCABC circumcircle. Let EE be such a point on ABAB, that CECE and ADAD are perpendicular and let FF be the second intersection of line ACAC and the circle CDECDE. Prove that DFDF and ABAB are parallel.
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