1. Draw a circle. Draw a line secant to the circle. Construct the points of intersection of the circle and the secant line.
2. Hide the secant line (not the two points that name the line). Construct the chord of the circle cut by the secant line (the points of intersection are the endpoints of this segment).
3. Construct a line perpendicular to this chord through the center of the circle. Construct the radius made by the point of intersection of the circle and the perpendicular line. Construct the point of intersection (G) of the perpendicular and the chord.
4. Construct segments EG and GF. Measure the segments.
Is there a relationship between the lengths of these segments? If so, what is the relationship?
Move point C to move the chord. How does the relationship of these segments compare to the original relationship?
5. Make a conjecture about the relationship
between a chord and the radius of a circle when they are perpendicular.
6. Below is a circle with two chords. Locate the center of the circle. Link to GSP to complete.
Explain the steps and constructions you used to locate the center of the circle.
Is your constructed center the center of the circle? How do you know?
Make a conjecture based on this investigation.