In a triangle \( \mathrm{ABC} \), the internal angle bisector of \(...

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In a triangle \( \mathrm{ABC} \), the internal angle bisector of \( \angle \mathrm{ABC} \) meets \( \mathrm{AC} \) at \( \mathrm{K} \). If \( \mathrm{BC}=2, \mathrm{CK}=1 \) and
\( \mathrm{P} \) \( \mathrm{BK}=\frac{3 \sqrt{2}}{2} \), then find the length of side \( \mathrm{AB} \).

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