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.

Statement 1 can't be true, as if Y was the center, then it wouldn't be possible for a circle to pass through all 3 points; D, F and N.

Statement 2 can't be true, for the same reason as statement 1. If Y was the center, it wouldn't be possible for a circle to pass through all 3 points; M, N and E.

Statement 3 can't be true, for the same reasons. If Y was the center, it wouldn't be possible for a circle to pass through all 3 points; L, M and N.

Statement 4 is the true answer, as it is possible for a circle to pass through all 3 points; D, E and F if Y was the center. Also, Y is the circumcenter of triangle DEF, so this statement must be true.