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

Amy`s construction will be correct. Beth`s start is appropriate for the construction of the circumscribed circle of the triangle.
After start she will have to find the point of intersection of all three angle bisectors, which will be the center of a circle inscribed in the triangle.
Finally, she will construct a desired circle.