Question

Draw an obtuse-angled triangle and a right-angled triangle. Find the points of concurrence of the angle bisectors of each triangle. Where do the points of concurrence lie?

Answer 1

I. Right angled triangle
Steps of construction
1. Draw a right angled triangle ABC, right angled at B.
2. Make the angle bisectors of the angles A, B and C.
The angle bisectors meet at the point O. This point of concurrence of the angle bisectors lies inside the triangle ABC.


II. Obtuse-angled triangle
Steps of construction
1. Draw an obtuse angled triangle XYZ.
2. Make the angle bisectors of angles X, Y and Z.
The angle bisectors meet at point S. This point of concurrence of the angle bisectors lies inside the obtuse angled triangle XYZ.