Point D, E, and F are not in a line. To contruct a circle through point D, E, and F, begin by drawing line egment DE and EF. Then contruct the perpendicular biector of DE and EF, and name the point of interection of the perpendicular biector O. How do you know that point O i the center of the circle that pae through the three point?

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07-12-2022
Mathematics

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Point D, E, and F are not in a line. To contruct a circle through point D, E, and F, begin by drawing line egment DE and EF. Then contruct the perpendicular biector of DE and EF, and name the point of interection of the perpendicular biector O. How do you know that point O i the center of the circle that pae through the three point?

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varshamittal029 varshamittal029 · Answer 1 · 2022-12-14T00:46:34+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.

To learn more about construction of a circle refer here

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