[Ananya Bhattacharya]

You can try to use the Exterior Bisector theorem.
Or try to find the sum of the angles formed by joining two pairs of intersection points is \(180^{\circ}\)

[Ananya Bhattacharya]

I mean for isosceles  triangle, the external angle bisector of the unequal angle will never meet the other side.

[Ananya Bhattacharya]

Can you please show with example of an obtuse angle with unequal sides how external bisectors of an angle can meet the opposite side?
unless i curve the plane of paper, this thing is beyond my ability to perceive or understand.
I can not prove that they will ever intersect the opposite sides according to Euclidean Geometry.

[Ananya Bhattacharya]

@Swastik Pramanik,
You can try to pick a Point and see what kind of integer coordinates they may have, ood or even or both, (with positions)
then u can think of picking another point that may take any of these and what will happen then to their mid point.

Try this, it is an interesting thought you may find.

[Ananya Bhattacharya]

It is a nice observation. 🙂

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