Question

Amy and Beth are both working on a construction of a circle inscribed in a triangle. Amy starts by finding the angle bisectors of each angle in the triangle. Beth starts by finding the perpendicular bisectors of each side of the triangle. Whose construction will be correct? What additional steps must be taken to complete the construction of the inscribed circle?

Answer 1

1.Draw the triangle.
2.Draw the angle bisector for each angle of the triangle. Draw the lines long enough so that you see a point of intersection of all three lines.

It seems that Amy has the correct procedure but also needs to do steps 3 and 4.

3.Draw a line perpendicular to any side that passes through the intersection point. Mark the point on the side through which this line passes.
4.Draw the circle with radius at the intersection point that passes through the point you obtained in the last step. This is the desired circle.

Source:
http://www.math.nmsu.edu/~pmorandi/CourseMaterials/InscribedTriangles.html