1. The problem asks to construct the three perpendicular bisectors of each triangle and show they are concurrent, meaning they intersect at a single point called the circumcenter. 2. The perpendicular bisector of a side of a triangle is a line that is perpendicular to that side and passes through its midpoint. 3. To construct a perpendicular bisector: - Find the midpoint of the side by averaging the coordinates of its endpoints. - Find the slope of the side. - The slope of the perpendicular bisector is the negative reciprocal of the side's slope. - Use the midpoint and perpendicular slope to write the equation of the bisector. 4. Repeat this for all three sides of the triangle. 5. Solve the system of equations of any two perpendicular bisectors to find their intersection point. 6. Verify that this intersection point lies on the third perpendicular bisector as well, confirming concurrency. 7. This point is the circumcenter, equidistant from all three vertices. Since the problem involves four triangles, the total number of distinct problems is 4. This explanation applies to each triangle individually.