Graphical Solution of a Quadratic Equation Using the Arithmetic and Geometric Mean

This Demonstration shows a graphical solution of the quadratic equation . If and are the solutions of the equation, then and . So is the arithmetic mean of and , and is the geometric mean.
Construct a triangle with vertical leg and hypotenuse . Let and be the intersection of the extension of the horizontal leg and the circle with center and radius .
Then and are the solutions of the equation.

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