Segments Lengths in Circles
1.
Observe circle G below, 2 chords intersect inside the circle. This breaks each chord up into 2 parts.
Drag and move the points to different positions and sketch what you see on your worksheet. Make sure to label your diagram.
Do you notice any relationship between the 4 parts of the chords?
- Multiply the length of CG by the length of GD.
- Now multiply the length of EG by the length of GF.
- What do you notice about the products above? Write an equation that represents this relationship.
**Try moving all points to a new position and observe whether the relationship still holds true.**
2.
Observe the diagram below, 2 secant lines intersect outside of a circle. This breaks each secant line into 2 parts.
Drag and move the points to different positions and sketch what you see on your worksheet. Make sure to label your diagram.
Do you notice any relationship between these four segments?
- Find the length of CD and ED.
- Multiply the length of CD by FD.
- Multiply the length of ED by GD.
- What do you notice about the products from above? Write an equation that represents this relationship.
**Try moving all points to a new position and observe whether the relationship still holds true.**
3.
In the diagram below, a secant line intersects a tangent line outside of the circle. The secant line is broken up into two parts. This is similar to the diagram above except that CD only has 1 section.
Drag and move the points to different positions and sketch what you see on your worksheet. Make sure to label your diagram.
What relationship do you notice about these line segments?
- Find the length of EC.
- Multiply the length of EC by the length of FC. (Round to nearest whole #)
- What is the relationship between this product of EC and FC, and the length of DC?
**Try moving all points to a new position and observe whether the relationship still holds true.**