pre college mathematics

[swastik pramanik]

(i) prove that the external bisectors of the angles of a triangle meet the opposite sides in three collinear points.

(ii) prove that the internal bisectors and the external bisector of the third angle meet the opposite sides in three collinear points?

[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]

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

[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 \(180^{\circ}\)

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