Pythagorean Theorem proof by Intersecting Chords Theorem
- Author:
- Bill Lombard
Pythagorean Theorem proof by Intersecting Chords Theorem
The Intersecting Chords Theorem states that if any two chords intersect in a
circle, then the products of their segments are equal. In our case, then FC ∙ CG = EC ∙ CD.
In terms of a, b, and c:
b ∙ b = (c - a)(c + a); using a little algebra,
b² = c² - a²; rewriting, we have the familiar a² + b² = c²
Pythagorean Theorem relationship in a right triangle.
credits:
http://peterashmathedblog.blogspot.com/2011/09/mathematics-and-humor.html
http://www.cut-the-knot.org/proofs/IntersectingChordsTheorem.shtml