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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 =__________