Question

Points X and Y are two different points on a circle.

Point M is located so that line segment XM and
line segment YM have equal length. Which of the
following could be true?
I. M is the center of the circle.
II. M is on arc XY.
III. M is outside of the circle.
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and II

Answer 1

Answer: E

Explanation:

For XM = YM, M needs to lie on the perpendicular bisector of XY, but this could be the center, on the arc, or outside of the circle.