Exploring Radii of Secants and Tangents
Observe how the angles a radius makes with a line change as the line shifts from a secant to a tangent.
Task 1
Putting It All Together
Answer these open ended questions on your own or with others to form deeper math connections.
Task 2
Why are the angles shown in the figure congruent?
Task 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?
Task 4
What do you observe about these angles at the exact moment the two points coincide and the line becomes a tangent?
Task 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?
Task 6
Use your answer to the latest question to formally prove that the tangent line is perpendicular to the radius.