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?

Students were asked to answer a question at academics and to say what is most important for them to succeed. One which response stood out from the rest was practice. Successful people absolutely not born successful; they become successful from hard work and persistence. If you want to fulfill your goals, keep this in mind! in this article, some question and answer examples that you may implement to improve your knowledge and gain insight that will assist you to keep up your school studies.

Question:

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?

Answer:

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.

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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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From the answer and question examples above, hopefully, they can guide the student take care of the question they had been looking for and take notice of all the stuff stated in the answer above. You may then have a discussion with your classmate and continue the school learning by studying the question mutually.

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