Question

point y is the circumcenter of triangle def. which statement is true about point y? point y is the center of the circle that passes through points d, f, and n. point y is the center of the circle that passes through points m, n, and e. point y is the center of the circle that passes through points l, m, and n. point y is the center of the circle that passes through points d, e, and f.

Explanation:

Step1: Recall circumcenter definition

The circumcenter of a triangle is the center of the circumscribed circle (circumcircle) that passes through all three vertices of the triangle.

Step2: Apply to triangle DEF

Point Y is the circumcenter of triangle DEF. So, the circle with center Y should pass through the three vertices of triangle DEF, which are D, E, and F.

Step3: Analyze each option

• Option 1: Passes through D, F, N – N is not a vertex of △DEF, so false.
• Option 2: Passes through M, N, E – M, N not vertices, false.
• Option 3: Passes through L, M, N – None are vertices, false.
• Option 4: Passes through D, E, F – These are the vertices, so true.

Answer:

Point Y is the center of the circle that passes through points D, E, and F.