Question

Jessica is using a compass and straightedge to construct the inscribed circle for triangle PQR. What should be her first step?

Answer 1

The first step in constructing the inscribed circle for triangle PQR using a compass and straightedge is to draw the perpendicular bisectors of two sides of the triangle.

Step-by-step explanation:

The first step in constructing the inscribed circle for triangle PQR using a compass and straightedge is to draw the perpendicular bisectors of two sides of the triangle. This will intersect at the center of the circle. Here are the steps:

1. Using a straightedge, draw a line segment that passes through the midpoint of side PQ and is perpendicular to PQ.
2. Repeat step 1 for side QR, drawing a line segment that passes through the midpoint of QR and is perpendicular to QR.
3. The point where the two perpendicular bisectors intersect is the center of the inscribed circle.
4. Use the compass to draw the circle with this center and a radius equal to the distance from the center to any vertex of the triangle.