Numerical [JEE Main-2021 (Jaly)] Consider a triangle having vertice...

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Numerical
[JEE Main-2021 (Jaly)]
Consider a triangle having vertices \( \mathrm{A}(-2,3), \mathrm{B}(1,9) \)
\( \mathrm{P} \) and \( \mathrm{C}(3,8) \). If a line \( \mathrm{L} \) passing through the circumcentre of triangle \( \mathrm{ABC} \), bisects line \( \mathrm{BC} \), and intersects \( y \)-axis at point \( \left(0, \frac{\alpha}{2}\right) \), then the value of real number \( \alpha \) is
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