Construct a circle through points x y and z

Steps to Construct a Circle Through Points x, y, and zGiven;

The number of given points = 3 x, y, and z

Method;

The given points can be taken as the vertex of a triangle, Δxyz

Solution;

The steps to draw an circumscribed circle of a triangle involve finding the

circumcenter of the triangle as follows;

1) Construct the perpendicular bisector of the three sides.

Place the compass at the endpoints of each side, and draw arcs that intersect above and below the side.Join the intersection points of the arcs to form the perpendicular bisector.

2) Place the compass point at the point of concurrency of two or three

perpendicular bisector, and open the compass to one of the vertices to

obtain the radius of the circle.

3) With the radius from the step above, draw a circle that passes through

the three given points to complete the circle.

Learn more about the circumscribed circle of a triangle here:

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1. Open the compass to a little more than halfway across the line segment XY. Draw an arc centered at the first endpoint X across the line segment XY. Without changing the width of the compass, place the compass tip on the second endpoint Y. Draw a second arc across the line segment XY.
2. Line up a straightedge with the intersection of the arcs above the line XY, and the intersection of the arcs below the line. Draw a line connecting these two points. The line you draw is a perpendicular bisector. It bisects the line XY at a right angle.
3. Use a compass and straightedge to construct the bisectors of the line YZ as you did with the first line segment. Extend the bisectors long enough that they intersect. The point of their intersection is the center of the circle.
4. The radius of a circle is the distance from the center to any point on the circle’s edge. To set the width, place the tip of the compass on the center of the circle, and open the compass to any one of your original points.Swing the compass around 360 degrees so that it draws a complete circle. The circle should pass through all three points.

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