Question

A circle passes through the points \( (1, 1) \) and \( (2, -1) \), and its center lies on the line \( x + y = 4 \). What is the radius of the circle?

• A. \( \sqrt{5} \)
• B. \( \sqrt{10} \)
• C. \( \sqrt{13} \)
• D. \( \sqrt{17} \)

Hint:

The center of the circle lies on the perpendicular bisector of the line joining the two given points.

Answer 1

The Correct Option is A

First, find the center of the circle. The center lies on the line \( x + y = 4 \), and the circle passes through two given points. Use the midpoint formula to find the center by averaging the coordinates of \( (1, 1) \) and \( (2, -1) \), and then use the distance formula to find the radius.