Objective: to explore the relationship between the angles formed with secants and tangents

Materials: GSP

Name ___________

Period ___________

Computer Station ____

1. Define the following

a) secant

b) tangent

2. Open GSP.

a) Construct circle C.

b)Point A is the tangent point. Recall that the tangent line is perpendicular to the radius. In order to constuct point E, first draw a radius. Then constuct the line that is perpendicular to the radius through point A.

c) Points B and D lie on the circle. Draw a line through D and B. This is your secant line. Mark the intersection point to the secant line and tangent line. This is point E.

d) At this point you may want to clean up your sketch. Construct segment connecting A and E. Constuct a segment connecting E and D. Now select the lines and the radius. Go under Display and go to Hide Objects.

2. Go to measure to determine the arc measures.

a) Measure arcs AD and AB. _________________________

b) Do you see any relation? ____________________________

c) Move point E to three other locations. Record your findings.

arc AD	arc AB	relationship

3. Now construct a tangent-tangent angle.

a) Construct circle C.

b) Draw two tangent lines. Refer back to step one to draw a tangent line.

c) Mark the intersection of the tangent lines as point D. Refer back to step one in order to draw a tangent line.

­BDC is the tangent-tangent angle.

d) Measure the major arc, minor arc, and the tangent-tangent angle. Move point B to two other locations and repeat the measurements.

	arc CB	arc CEB	­BDC
a)
b)
c)

e) Determine the relationship between the two arcs and the tangent-tangent angle.

4. Using your observations from the above problems, complete the following problems.

Return to Instructional Unit.