$A$ lies on the perpendicular bisector of $XC$ because

$A$ lies on the perpendicular bisector of $XC$ because
  1. $AX = AC$
  2. $AX = AB$
  3. $AX = BC$
  4. $XC = AB$

Solution

By construction $BX = AB - AC$, and since $A$ lies on the ray, $BA = BX + XA \Rightarrow XA = AC$.

Asked in: MH-SSC-9

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