A line that intersects a circle in exactly one point is called a tangent to the circle. You can use this activity to explore some of the characteristics of tangents.
Measure CD and CE (by selecting the points). What do you notice?
CD is the same length as CE. Two tangents from a common point are equidistant (the same distance to the circle)
Drag point C around. Do lines CD and CE appear to be tangent to circle A?
Measure angles CEA and ADC. How do you think the tangent line is related to the radius at the point of tangency?
The radius is perpendicular to the tangent line at the point of tangency!
Now you try! Construct a circle with 2 tangent lines from a common point. [br]Measure the segments to be sure they are the same distance.[br]Construct the two radii to the points of tangency.[br]Measure the angles at the points of tangency to be sure they are correct.[br]
Select "Check your answer" to see the notes you should copy into your textbook:
[br][br]Two tangent lines from a common point are [b][i]equidistant[/i][/b][br][br]Tangent lines are perpendicular to the radius.[br][br][br]