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Triangle $A^*BC$ is a right angled isosceles triangle and $A^*B$ is perpendicular to $BC$.The line $B^*B$ is perpendicular to the plane $A^*BDC$ so it is perpendicular to $BC$. As the two line $A^*B$ and $B^*B$ are perpendicular to $BC$ the whole plane $AB^*BA^*$ is perpendicular to $BC$. Hence $AB$ is perpendicular to $BC$. |