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### Course: Geometric Properties with Equations & Circles 241+>Unit 3

Lesson 10: Properties of tangents

# Proof: Radius is perpendicular to tangent line

Sal proves that the radius that connects the intersection point of a tangent line with the circle is perpendicular to the tangent line.

## Want to join the conversation?

• At , what is a non degenerate triangle? (And, if it exists, what is a degenerate triangle?)
• I looked this up on Google.
A degenerate triangle is "a "triangle" formed by 3 collinear points. It doesn't look like a triangle. It looks like a line segment."
In the video, if b were zero, side c would collapse back onto side a.

So, bearing this in mind, I guess that a "non-degenerate" triangle is the usual type of triangle that we see. It would be formed when not all 3 points were collinear.
• Why is this necessary to prove? I mean, can't this just be intuitively thought of using the definition?
• That is how proofs in Math work. You start by proving ideas that are so so basic that they are common sense and then proceed to more difficult proofs. Plus, in Math you can't say this is intuitively true unless it is a postulate( something assumed to be true that can't be proved).
• Can someone explain in a easier way had a hard time understanding.
• basically a line that does not go through the circle but is on the circle is a tangent. A radius that connects to the tangent is 90 degrees.
• This might be a silly question but I was wondering if a line could touch two adjacent points with no space between them (if that even makes sense) on a circle, without crossing it. Is that possible? Would that also be considered tangent?
• You are right that it is a little confusing. Adjacent means next to, so by definition, there has to be some space between them, but it could be really really close to each other. If a line touches the circle at a single point, it could not touch two lines, otherwise you would form an arc which could also be very small. A tangent could only touch one of the points, but once again the other point could be very close to the line.
• Can we prove this by using triangle inequality theorem?
• I am not sure about that because triangle inequality is valid for any triangle in the plane. Here you are strongly using the fact that you actually can construct a right triangle, which is a particular kind of triangle. Then Sal is showing that a<c.
• Wait, no explanation or definition about a tangent line?? In calculus, a tangent line is a straight line that touches a function at only one point (I googled because I haven't learned it yet), but what about in geometry? I need some explanation before proving.
• Same definition, only it's used mainly for circles in geometry (compared to functions in Calculus). So in geometry you'll most likely see "the tangent line to this circle," which just means the line that touches the circle at a single point.
• what low or a mathematical rule can we use when we see tangent line in a circle or a triangle
• Laws of triangles state that the hypotenuse is the longest side. See in this video.
• How did you know that the right triangle's leg was going to be the shortest distance away from the center point?