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.
Offene Frage 1
Why are the angles shown in the figure congruent?
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Offene Frage 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?
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Offene Frage 3
What do you observe about these angles at the exact moment the two points coincide and the line becomes a tangent?
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Offene Frage 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?
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Offene Frage 5
Use your answer to the latest question to formally prove that the tangent line is perpendicular to the radius.
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