Name ________________________________
Date ____________________
Lab: Exploring Tangent Lines with Geometer's Sketchpad
Part 1 - Tangents and Radii
Objective: To investigate the angle formed by the tangent and the radius of a circle.
1. Using the circle and segment tools, construct circle A with radius AB.
2. Using the point and line tools, construct a point C on the circle and draw a secant that runs through B
and C.
3. Measure the ∠ABC that is formed.
4. Select point C and move it around the circle until the line BC is tangent to the circle. What is the
m∠ABC now?___________________________ ____________________________________
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5. What conjecture can you make about a tangent and a radius to the point of tangency?
__________________________________________________________________________________
______________________________________________________________________________
6. Use this conjecture to construct a tangent line to a circle at a given point P.
Geometry – Circles
-1-
NJCTL.org
Part 2 - Tangent Segments
Objective: To investigate the relationship between tangent segments.
1. Using the circle and segment tools, construct circle A with radius AB.
2. Using the perpendicular line tool, construct a tangent line t through B.
3. Construct another radius AC and a tangent line s through C.
4. Construct and label the point where lines s and t intersect as point D.
5. Measure the tangent segments DB and DC. What relationship exists?__________________________
__________________________________________________________________________________
6. Select point B and move it around the circle. What happens to the segment measures of DB and
DC?_____________________________________________________________________________
__________________________________________________________________________________
7. What conjecture can you make about tangent segments from the same exterior point?
__________________________________________________________________________________
__________________________________________________________________________________
Geometry – Circles
-2-
NJCTL.org