Instructions: Below is Circle D (black) with chord GF (blue). Line f (red) is the perpendicular bisector of GF. Use this sketch to complete the questions below.
Theorem: The perpendicular bisector of a chord always passes through the center of the circle.
Prove why this is true.
Now we are going to construct a circle through 3 noncollinear points.
Complete the construction.
(Do not simply use the "circle through 3 points" button)
Prove why this is true.
Now we are going to construct a circle through 3 noncollinear points.
- Draw 3 points F, G, and H
- Draw the segments FG and GH
- Construct the perpendicular bisector of each of the segments
Complete the construction.
(Do not simply use the "circle through 3 points" button)