Points D, E, and F are not in a line. To construct a circle through points D, E, and F, begin by drawing line segments ("DE" ) ̅ and ("EF" ) ̅. Then construct the perpendicular bisectors of ("DE" ) ̅ and ("EF" ) ̅, and name the point of intersection of the perpendicular bisectors O. How do you know that point O is the center of the circle that passes through the three points?

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22-07-2017
Mathematics

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Points D, E, and F are not in a line. To construct a circle through points D, E, and F, begin by drawing line segments ("DE" ) ̅ and ("EF" ) ̅. Then construct the perpendicular bisectors of ("DE" ) ̅ and ("EF" ) ̅, and name the point of intersection of the perpendicular bisectors O. How do you know that point O is the center of the circle that passes through the three points?

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aksnkj aksnkj · Answer 1 · 2021-11-28T12:02:41+01:00

The perpendicular from the center to a secant of a circle will bisect the secant. The intersection of perpendicular bisectors will be the center of the given circle passing through D, E, and F.

Points D, E, and F are not in a line. It is required to construct a circle through points D, E, and F.

The given construction steps are:

Draw line segments ("DE" ) and ("EF" ).
Construct the perpendicular bisectors of ("DE" ) and ("EF" ).
Name the point of intersection of the perpendicular bisectors O.

The point O will be the center of the circle passing through the points D, E, and F.

The above conclusion is because the perpendicular from the center to a secant of a circle will bisect the secant. Here, both the perpendicular bisectors will pass through the center of the circle and hence, their intersection will be the center of the given circle passing through D, E, and F.

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