NAME __________________________
GSP 10.1
Activity I Point of Tangency
Step 1:
Step 2:
Construct a circle with center A and radius endpoint B.
Construct radius AB.
Step 3:
Step 4:
Step 5:
Construct point C on the circle.
Construct secant BC.
Measure angle ABC.
Drag point C around the circle toward point B. Watch the measure of angle ABC as point C gets closer to point B. What is the measure of the angle when point C is right on top of point B? _________. When points B and C coincide, your line intersects the circle in a single point so it is tangent to the circle. What is the relationship between the radius and the tangent line at the point of tangency?
______________________.
If you wish to construct a tangent to a circle, construct the radius first, select the radius and the pint of tangency and construct a ____________ line.
Activity II
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Step 6:
Construct circle AB (center A and radius endpoint B) and radius
AB.
Construct a tangent through B.
Construct a second radius AC.
Construct a tangent through C.
Label the point where the two tangents intersect D.
Step 7:
Step 8:
Step 9:
Construct segments BD and CD. Be sure to construct the segments so that when you hide the lines the segments will stay.
Hide the lines. You now have tangent segments.
Measure the lengths BD and CD. Move points C, B, or A to see if this relationship holds for all segments to a circle from a point outside the circle.
Construct AD

What are the measures of angles ABD and ACD? ____________ Why is AB congruent to AC? ________________ Is triangle ABD congruent to triangle ACD?
_________ By what reason? ____________

GSP 10.1 Continued
Activity III
Step 1: Sketch two circles that are internally tangent. Draw a tangent line at the point where the two circles intersect. Is the common tangent internal or external? _________
Step 2: Sketch two circles that are externally tangent. Draw a tangent line at the point where the two circles intersect. Is the common tangent internal or external? ___________
Note! Review definitions of a common internal tangent and a common external tangent.