Observe circle G below, 2 chords intersect inside the circle. This breaks each chord up into 2 parts. [br][br]Drag and move the points to different positions and sketch what you see on your worksheet. Make sure to label your diagram.[br][br]Do you notice any relationship between the 4 parts of the chords?[br][br][list][*]Multiply the length of CG by the length of GD. [/*][/list][list][*]Now multiply the length of EG by the length of GF.[/*][/list][list][*]What do you notice about the products above? Write an equation that represents this relationship.[/*][/list][size=100][size=85][i][center][/center][center]**Try moving all points to a new position and observe whether the relationship still holds true.**[/center][/i][/size][/size]
Observe the diagram below, 2 secant lines intersect outside of a circle. This breaks each secant line into 2 parts. [br][br]Drag and move the points to different positions and sketch what you see on your worksheet. Make sure to label your diagram.[br][br]Do you notice any relationship between these four segments?[br][list][*]Find the length of CD and ED.[/*][/list][list][*]Multiply the length of CD by FD. [/*][/list][list][*]Multiply the length of ED by GD.[/*][/list][list][*]What do you notice about the products from above? Write an equation that represents this relationship.[/*][/list][center][i][size=85]**Try moving all points to a new position and observe whether the relationship still holds true.**[/size][/i][/center]
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. [br][br]Drag and move the points to different positions and sketch what you see on your worksheet. Make sure to label your diagram.[br][br]What relationship do you notice about these line segments?[br][list][*]Find the length of EC.[/*][/list][list][*]Multiply the length of EC by the length of FC.[i] (Round to nearest whole #)[/i][/*][/list][list][*]What is the relationship between this product of EC and FC, and the length of DC?[/*][/list][i][size=85][center]**Try moving all points to a new position and observe whether the relationship still holds true.**[/center][/size][/i][br]