To construct a circle given three points

Given: Points A, B, C

Required: To construct a circle containing given points A, B, C.

Procedure:

construct a circle given 3 points

Use the segment command under the construct menu, to construct segments AB, BC, and CA. You now have a triangle,

ABC with points A, B, and C as vertices.

Construct the perpendicular bisectors of two sides of the triangle. This can be accomplished by following the basic perpendicular bisector construction; (help, midpoint) (help,

) or by using the tools in Sketchpad which follows:

Select segment AB.

Use the midpoint command under the construct menu to place a midpoint on AB. Label it D.

Select the midpoint D and segment AB, use the perpendicular line command under the construct menu and construct a perpendicular at D.

Select segment BC and repeat the above steps, but label the midpoint E.

Label the point of intersection of the two perpendicular bisectors point F.

Use the segment command under the construct menu and construct segment FB.

Use the circle by center + radius command under the construct menu and construct a circle with center F and radius congruent to segment FB.

This is the required circle.

Proof:

F the intersection of the

bisectors.

Segment FB = FA = FC (The

bisector of the sides of a triangle are concurrent in a point equidistant from the vertices)

A, B, and C all lie on the same circle. (definition of circle)

Sketch: Drag points A, B, or C around on the sketch below. Does the circle still contain all 3 points?

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circle given three points

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