Segments Lengths in Circles
Chords intersecting in a circle.
In the picture below 2 chords intersect inside the circle.
This breaks each chord up into 2 parts.
Do you notice any relationship between the 4 parts of the chords?
Now multiply the length of CG by the length of GD. Write that value here __________.
Now multiply the length of EG by the length of GF. Write that value here __________.
What do you notice about the products above?
Now move all 4 points of the circle to a new position. (Make sure that the chords still intersect.)
Now multiply the 2 parts of each chord together and see if you get the same result as above.
Product 1: __________ Product 2: ___________
Secant Lines Intersecting Outside of a Circle
In the picture below 2 secant lines intersect outside of a circle.
This breaks each secant line into 2 parts.
Do you notice any relationship between these four segments?
Now find the length of CD and ED and write the here. CD = ________ ED = ________
Multiply the length of CD and FD together and write the product here. ___________
Multiply the length of ED and GD together and write the product here. ____________
What do you notice about the products from above?
Now move point C, point E and point D to new locations.
Perform the same process from above and see if you get the same results.
CD=________ ED=_________ Product of CD and FD=_________ Product of ED and GD=_________
Secant Tangent Line Intersections
In the figure 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 figure above except for CD only has 1 section.
Find the length of EC and write it here. EC = ________
Multiply the length of EC by the length of FC. Write the product here ___________. (round to the nearest whole number)
What is the relationship between this product and the length of DC?
Move point C, E and D around to new positions and see if the relationship from above is still true.
EC = _________ Product of EC and FC =_________ DC squared =__________