Final answer:
To construct an inscribed circle in triangle PQR, you need to find the incenter by bisecting the angles of the triangle, then use this point to draw the circle that is tangent to all three sides of the triangle.
Step-by-step explanation:
The task is to construct an inscribed circle (also known as an incircle) in a triangle PQR by finding the incenter of the triangle. The incenter is the point where the angle bisectors of a triangle intersect, and it serves as the center of the circle inscribed within the triangle. The steps are as follows:
- Bisect each angle of triangle PQR using a compass and straightedge.
- The point where all three angle bisectors meet is the incenter of the triangle.
- Using the incenter as the center point, adjust your compass to reach any of the triangle's sides and draw the circle. This will be your incircle, touching all three sides of the triangle (tangent).
The properties of similar triangles are not directly related to this construction; however, they can be involved in proof related to the properties of incircles.