Question

describe how to construct the center of a given circle if the center is not marked. choose the correct answer below. a. pick any three points a, b, and c on the circle and construct the perpendicular bisectors of ab and ac. the intersection of the perpendicular bisectors is the center. b. pick any three points a, b, and c on the circle such that △abc is an equilateral triangle. the center is the point d in the circle where all four points are equidistant from each other. c. pick four points a, b, c and d on the circle such that ab and cd intersect. the intersection of ab and cd is the center. d. pick any two points a and b on the circle. the point c where ac = bc is the center.

Explanation:

The center of a circle is equidistant from all points on the circle. The perpendicular bisector of a chord (a line segment whose endpoints lie on the circle) passes through the center of the circle. By constructing the perpendicular bisectors of two different chords (formed by choosing three points on the circle), their intersection gives the center.

Answer:

A. Pick any three points A, B, and C on the circle and construct the perpendicular bisectors of $\overline{AB}$ and $\overline{AC}$. The intersection of the perpendicular bisectors is the center.