# AB-circle diameter A (3; 7) B (5; 1) Find the center coordinates and radius.

July 24, 2021 | education

| If C is the center of the circle in which the segment AB is the diameter, then the point C divides the segment AB in half and the coordinates of point C are equal to the half-sums of the coordinates of points A and B:

C ((3 + 5) / 2; (7 + 1) / 2) = C (4; 4).

The radius of the circle is equal to half the length of the diameter AB:

r = 0.5 * ((5 – 3) ^ 2 + (1 – 7) ^ 2) ^ 0.5 = 0.5 * 40 ^ 0.5 = 10 ^ 0.5 = 3.162.

Answer: C (4; 4), r = 3.162.

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