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Draw an obtuse-angled triangle and a right-angled triangle. Find the points of the concurrence of the angle bisectors of each triangle. Where do the points of concurrence lie?
Point of the concurrence of bisectors of obtuse angle and right angle:
In order to construct an angle bisector following steps should be followed
STEPS:
1. Place the compass point on the vertex of the angle (point B).
2. Stretch the compass to any length that will stay on the angle.
3. Swing an arc so the pencil crosses both sides (rays) of the given angle. You should now have two intersection points with the sides (rays) of the angle.
4. Place the compass point on one of these new intersection points on the sides of the angle.
If needed, stretch the compass to a sufficient length to place your pencil well into the interior of the angle. Stay between the sides of the angle. Place an arc in this interior.
5.Now, without changing the span on the compass, place the point of the compass on the other intersection point on the side of the angle and make a similar arc. The two small arcs in the interior of the angle should be intersecting.
6. Connect the vertex of the angle (point B) to this intersection of the two small arcs.
You now have two new angles of equal measure, with each being half of the originally given angle.
Following the above method,
The angle bisectors of an obtuse-angled triangle intersect at a point M inside the triangle.
The angle bisectors of a right-angled triangle intersect at a point N inside the triangle.
In the figure, ABC is an obtuse-angled triangle whose angle bisectors intersect at point M and it lies inside the triangle. PQR is a right-angled triangle whose angle bisectors intersect at point N and it lies inside the triangle.
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