2.(2) A(- 1, 0) B (3,0) C (0,3) Circle N passes through three points A, B and C, so it is the circumscribed circle of triangle ABC. Now, find the center of the circumscribed circle of triangle ABC, that is, the intersection point of the perpendicular lines of three sides. A(- 1, 0) b (3,0) are all on the X axis, so the perpendicular of AB is x= 1. OB=OC, so the midline of BC passes through point O (0,0) and point (1.5, 1.5), so the midline of BC is Y = X, now we just need to find the intersection of straight lines x= 1 and y = X.

So the coordinate of the center point n is (1, 1).

3. According to the distance formula between two points, we know that under NC= root number: (0- 1) 2+(3- 1) 2 = root number 5,

So EC = 2nc = the root number 5 of 2.