Exploring Radii of Secants and Tangents
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.
Putting It All Together
Answer these open ended questions on your own or with others to form deeper math connections.
Open-ended question 1
Why are the angles shown in the figure congruent?
Text and math input
Open-ended question 2
As you move the two points closer together, what happens to the measures of the two angles formed by the radii and the line?
Text and math input
Open-ended question 3
What do you observe about these angles at the exact moment the two points coincide and the line becomes a tangent?
Text and math input
Open-ended question 4
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?
Text and math input
Open-ended question 5
Use your answer to the latest question to formally prove that the tangent line is perpendicular to the radius.
Text and math input
Explore more
Prerequisite Resources
More from Arc, Chord, and Tangent Properties of Circles
