Equilateral triangles $ABX$ and $CAY$ are described on sides $AB$ and $AC$ of a $\triangle ABC$ externally to $\triangle ABC$. Prove that $CX = BY$. > Equilateral triangles $ABX$ and $CAY$ are described on sides $AB$ and $AC$ of a $\triangle ABC$ externally to $\triangle ABC$. Prove that $CX = BY$. I constructed the following figure for it. ![enter image description here]( I am not able to proceed any further. How could I do this?

**Hint** : $\triangle ACX$ and $\triangle BAY$ are equal to each other: $$|AC|=|AY|, |AX|=|AB|$$and $Â$ in $\triangle BAY $ is equal to $Â$ in $\triangle ACX$ because $\triangle ABX$ and $\triangle ACY$ are equilateral triangles.