Simple and Understandable Proof | A Tangent Line is Perpendicular to the Radius | Circle

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Many people know the fact that a tangent line to a circle is perpendicular to the radius that connects the tangent point and the center of the circle, but it is challenging to prove. This math tutorial video shows you a simple and understandable proof for the fact.

Math
Mathematics
Geometry
Trigonometry
  1. Math Tricks
  2. circle
  3. radius
  4. tangent line
  5. tangent
  6. tangent point
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Thank you SO much, Dr. Liang. I was shown a very elegant proof using implicit differentiation for which I am very grateful, but I do prefer a proof using only geometry. I watched the video several times, and I took several screenshots to save your great work. Thanks again. :)

BlipBlop
Автор

Yes, so by definition a tangent line intersects a circle exactly once. If R is a point outside the circle OR is of course longer than OH. By the Fact, OH is perpendicular to the tangent line.

BlipBlop