In this activity students explore the locus of a point that is located twice as far from a given point A as it is from given point B. The locus is Apollonius circle. Students discover that the locus is a circle and then prove it. The key property: If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides.
Before the Activity
Before carrying out this activity teacher should review with the students the concepts of angular bisector, internal and external angles of polygons, and the equation of a circle.
During the Activity
The Word document is a teacher file that the teacher should use to facilitate this activity in class. The student .tns file can be used by students to follow along in this teacher-led activity.