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>Circles>How to Study the Power of a Point Theorem with GeoGebra

How to Study the Power of a Point Theorem with GeoGebra

You can use GeoGebra to study the power of a point theorem.

GeoGebra Instruction 1

1.: Open Algebra View and Graphics View under View in Menu.
2.: Select Circle through 3 Points (it is located in the same menu as Circle with Center through Point ) to construct the circle. The three points $A$ , $B$ , and $C$ you used for making the circle are going to be utilized in the next steps.
3.: Use Line to make a line through $A$ and $B$ .
4.: Use Point on Object (it is located in the same menu as Point ) to make a point $P$ on the line through $A$ and $B$ . The point is automatically called $D$ . If you want to change the name from $D$ to $P$ , right-click on $D$ and click on Rename. Type $P$ in the field and click OK.
5.: Use Line to make the line through $P$ and $C$ .
6.: Use Intersect to make $D$ by finding the point of intersection of the circle and the line you made in the previous step.
7.: Use Segment (it is located in the same menu as Line ) to make the segments $A C$ and $B D$ .
8.: If you want to remove the labels on the lines, line segments, and circle, right-click on Lines, Segments and Circle respectively and click on Show Label so that the check mark disappears.

Screenshot of GeoGebra showing two lines through the point P intersecting a circle

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