Analytic Geometry on GeoGebra – Circles

Click on the link for the Analytic Geometry on GeoGebra Applet

Part 1: The Right Bisector of a Chord.

§ Use the circle tool to make a circle.

§ Use the Line Segment tool to make a line segment from one end of the circle to the other. Do not make a diameter line (a line through the middle of the circle). This line is called a Chord.

§ Use the Right Bisector tool to make a right bisector of the circle. Notice that it goes through the centre of the circle.

§ Try this out with another circle and another chord.

Geometry Fact: The right bisector of a chord of a circle passes through the centre of the circle.

Part 2: The Right Bisectors of Two Chords.

§ Make a circle, and then make two chords.

§ Make the perpendicular bisectors of both chords.

§ They should intersect at the centre of the circle.

§ Try it again with a different circle and different chords.

Geometry Fact: The right bisectors of two chords of a circle intersect at the circle’s centre.

Part 3: How to Make a Circle from Three Points.

• Use the Point tool to make three non-collinear points (points that are not on the same line).
• Use the line segment tool to join the first point to the second, and the second point to the third.
• Make a perpendicular bisector of these two lines.
• Use the Intersection tool to put a point where these two lines intersect.
• Use the Circle tool to create a circle, the centre of which is the intersection of the two perpendicular bisectors. The circle centred at this point should go through all three points.
• Try it again.

Geometry Fact: There is only one circle that passes through three given non-collinear points.

All Done!