Question

1. using constructions find the circumcenter of the given δ.

Explanation:

Step1: Bisect one side

Use a compass to construct the perpendicular - bisector of one side of the triangle. Place the compass at each end - point of the side, draw arcs above and below the side, and then draw a line through the intersection points of the arcs.

Step2: Bisect a second side

Repeat the process for a second side of the triangle. Construct its perpendicular - bisector.

Step3: Find the intersection

The point where the two perpendicular - bisectors intersect is the circumcenter of the triangle.

Answer:

The intersection point of the perpendicular - bisectors of the sides of the triangle.