Final answer:
To construct the incircle of a triangle, the first step is to find the angle bisectors of the triangle, whose intersection determines the circle's center.
Step-by-step explanation:
The first step to constructing the inscribed circle of a triangle, also known as the incircle, is to find the angle bisectors of each angle of the triangle. These angle bisectors will intersect at a single point inside the triangle, which is the center of the inscribed circle. From this center, you can draw perpendiculars to each side of the triangle; the points at which these perpendiculars meet the sides of the triangle will be the points of tangency. The final step is to draw a circle with a compass, centered on the intersection of angle bisectors and with a radius that reaches any one of the tangent points.