Question

The figure shows a circle inscribed in a triangle.

A circle is inscribed within a triangle.

To construct the inscribed circle, angle bisectors were first constructed at each angle of the triangle. Which happened next?

A circle was constructed using the intersection of the angle bisectors as the center of the circle and the obtuse vertex as a point on the circumference of the circle.
A circle was constructed using a vertex as the center of the circle and the intersection of the angle bisectors as a point on the circumference of the circle.
Segments perpendicular to the sides of the triangle through the intersection of the angle bisectors were constructed.
Segments bisecting each side of the triangle were constructed through the intersection of the angle bisectors.

Answer 1

Segments perpendicular to the sides of the triangle through the intersection of the angle bisectors were constructed.

Reason: the intersection of the angle bisectors is the incenter. You drop perpendiculars from the incenter to the triangle's sides to get the radius (and tangent points); then draw the circle centered at the incenter with that radius. The other choices are incorrect (vertices are not used as center or tangent points, and bisecting sides is unrelated to the incircle construction).