Question

Consider a triangle having vertices $A(–2,3),B(1,9)$ and $C(3,8)$. If a line $L$ passing through the circumcenter of triangle $ABC$, bisects line $BC$, and intersects $y$-axis at point $\left(0.\frac{\alpha }{2}\right),$ then the value of real number $\alpha$ is

Answer 1

Line $L$ is perpendicular bisector of $BC$, which is
$L:4x–2y+9=0$
$L$ cuts the $y$-axis at $\left(0.\frac{9}{2}\right)$
Clearly, $\alpha =9$