Why do we use HALF the angles $\dfrac{\angle B}{2}$ and $\dfrac{\angle C}{2}$ in this construction?

Why do we use HALF the angles $\dfrac{\angle B}{2}$ and $\dfrac{\angle C}{2}$ in this construction?
  1. Because of the isosceles property: $AB = XB$ and $AC = YC$
  2. To make construction simpler
  3. Because angles are doubled in arcs
  4. Random choice

Solution

$\triangle XBA$ is isosceles with $XB = AB$, and bisecting gives correct construction.

Asked in: MH-SSC-9

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