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### Course: Class 10 (Foundation)>Unit 12

Lesson 1: Chords in circles

# Proof: radius is perpendicular to a chord it bisects

Sal proves that if a radius in a circle is drawn so it bisects a chord, then the radius is also perpendicular to that chord. The proof uses SSS congruence. Created by Sal Khan.

## Want to join the conversation?

• WHAT IS THE DEFFINITION OF A CHORD?
A Chord is a line segment which connects two points on a circle.
or
A Chord is a line segments whose endpoints are points on the coircle.
or
A Chord is a straight line joinng two points on the circumference of a circle.
Diameter is also a chord and it is the longest, the reason why it is not called a chord because it passes from the centre of the circle.

Hope that helps you.........
• What are corollaries and lemmas? Are they just theorems used for specific purposes?
• A corollary is basically another theorem that can extremely easily be proved with the first one. A lemma is like a proof of a theorem inside of a theorem (mostly used for lesser-known or less useful theorems that generally aren't actually considered theorems)!
• What does Sal mean when he says that line AE is equal to itself?
• That is the Law of Identity (abbreviated LOI). It is sometimes used in geometry proofs when the same line, line segment, angle or other measure is used in two different figures. The Law of Identity states that every figure is congruent to itself.

For example, In a proof that two triangles are congruent, if you already know that two sides are congruent and you have the two triangles sharing the third side, then you can establish SSS congruency by pointing out that the remaining side of each triangle must be congruent due to LOI.
• In the beginning of the video, Sal said that the previous video was about SSS congruence. But for me, it's the inscribed quadrilaterals proof. Just to be clear, I'm watching the video through Math => High School Geometry => Circles => Proofs with inscribed shapes. Am I missing something??
• No, he might have talked about SSS in the previous video even though the title does not say so. Don't worry about it too much, you probably already know what SSS means (Side side side congruence).
• What is the difference between theorems and postualtes?
• Both theorems and postulates are statements of truth, but the difference is that postulates are assumed to be true without proof, while theorems must be proven true. For example, the statement "a line contains at least two points" is a postulate. It is nearly a part of the definition of a line, and as a result, it requires no proof.

However, the statement "if two lines intersect, then they must intersect at only exactly one point" is a little less obvious. This is a theorem, because it must be proven before it is accepted as true.

http://www.cliffsnotes.com/math/geometry/fundamental-ideas/postulates-and-theorems
• I still don't understand:
What is an axiom and a postulate?
• An axiom or postulate are basically the same. They are things just assumed to be true and self-evident.
• Whats the difference between a postulate and an axiom? Are they the same thing?
• An axiom/postulate is always true, just as we know 1+1 is always 2. However, a theorem is built from combining the use of axioms and postulates. So if we know 1+1 is 2, 2+1 is 3, 3+1 is 4, we know that 1+1+1+1 is 4.
(1 vote)
• Somewhere in the video (probably where he drew the chord on the circle) he said something about secant? what is that?
• The term "secant" is used in mathematics in more than one way. In this case, it means a line that (locally) intersects the curve in exactly two places.

"Secant" (abbreviated "sec") is also the name a trigonometric function this is the reciprocal of the cosine.
Thus sec θ = 1 / cos θ