Geometry · Equilateral triangle · Perpendicular bisector · Congruent triangles · Rotational symmetry
On the sides \(AB\) and \(BC\) of an equilateral triangle \(ABC\), points \(Z\) and \(X\) are chosen so that
\[ AZ : ZB = BX : XC = 2021 : 2020. \]
The perpendicular bisector of the segment \(XZ\) meets the side \(AC\) at a point \(Y\). Determine the ratio \(AY : YC\).
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Serbian Regional Competition (Okruzno takmicenje) 2021, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source