To get the third vertex $A$ in this construction, we use the fact that $A$ lies on

To get the third vertex $A$ in this construction, we use the fact that $A$ lies on
  1. the perpendicular bisector of segment $XC$ (where $BX = AB+AC$ along the angle ray)
  2. the angle bisector
  3. a circle through $B$
  4. the median

Solution

Standard construction trick: lay off the sum, then take perpendicular bisector.

Asked in: MH-SSC-9

Practice more Constructions of Triangles questions on Aicharya