I. Tangents.
1. Use the Circle with Center through Point tool to construct a circle centered at point A.
2. Use the New Point tool to construct point C on circle A.
3. Use the Tangents tool to construct the line tangent to circle A at point C.
4. Drag point C along the circle and observe the tangent line. Define a tangent line.
5. Use the Segment Between Two Points tool to construct radius AC.
Describe the relationship between the tangent line and radius passing through the point of tangency.
6. Construct point D on circle A; then construct the line tangent to circle A at point D.
7. Use the Intersect Two Objects tool to construct point E, the intersection of the two tangent lines.
8. Construct segments CE and DE and change their colors.
9. Make a conjecture about the relationship between segments CE and DE. Test your conjecture
by measuring the segments and dragging the tangent lines.
II. Chords and Arcs. The circle below was constructed such that angle COD is congruent to angle BOA.
1. If two central angles are congruent, how are their chords related? Test your conjecture. Explain how you would prove your conjecture.
2. If two chords are congruent, how are their arcs related? Test your conjecture.
3. If two arcs are congruent, how are their central angles related? Test your conjecture.
4. If two chords are congruent, how are their distances from the center related? Test your conjecture.
1. In a circle, a diameter that is perpendicular to a chord __________ the chord and its arcs.
2. In a circle, a diameter that bisects a chord (that is not a diameter) is __________ to the chord.
3. In a circle, the perpendicular bisector of a chord contains the __________ of the circle.