A circle has a center at 4 – 5i and a point on the circle at 19 – 13i. Which of the following points is also on the circle?

The radius is the distance from the center, 4 − 5i, to the given point, 19 − 13i. Their real and imaginary parts differ by 15 and −8, so the radius is √(15² + (−8)²) = √289 = 17. Choice C, 12 + 10i, differs from the center by 8 and 15, and √(8² + 15²) = 17, so it lies on the circle.

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