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Let AB C D be a square of side of unit length. Let a circle \( C_{1} \) cantered at \( A \) with unit radius is drawn. Another circle
\( \mathrm{P} \)
\( \mathrm{C}_{2} \) which touches \( \mathrm{C}_{1} \) and the lines \( A D \) and \( A B \) are tan-
W) gent to it, is also drawn. Let a tangent line from the point \( C \) to the circle \( C_{2} \) meet the side \( A B \) at \( E \). If the length of \( \mathrm{EB} \) is \( \alpha+\sqrt{3} \beta \), where \( \alpha, \beta \) are integers, then \( \alpha+\beta \) is equal to
[JEE Main-2021 (March)]
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