A triangle is inscribed in a semicircle of diameter 2R, as
Chapter 4, Problem 57(choose chapter or problem)
A triangle is inscribed in a semicircle of diameter 2R, as shown in the figure. Show that the smallest possible value for the area of the shaded region is (p 2)R2 /2. Hint: The area of the shaded region is a minimum when the area of the triangle is a maximum. Find the value of x that maximizes the square of the area of the triangle. This will be the same x that maximizes the area of the triangle.
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