Relating Radii to Secants and Tangents
Observe how the angles a radius makes with a line change as the line shifts from a secant to a tangent.
Aufgabe 1
Putting It All Together
Answer these open ended questions on your own or with others to form deeper math connections.
Aufgabe 2
Why are the angles shown in the figure congruent?
Aufgabe 3
As you move the two points closer together, what happens to the measures of the two angles formed by the radii and the line?
Aufgabe 4
What do you observe about these angles at the exact moment the two points coincide and the line becomes a tangent?
Aufgabe 5
If you pick a point on the tangent line (other than the point of tangency), would its distance to the center be greater than, less than, or equal to the radius? Why?
Aufgabe 6
Use your answer to the latest question to formally prove that the tangent line is perpendicular to the radius.