Triangle and Circle with same CenterDate: 7/8/96 at 9:6:16 From: Anonymous Subject: Find the length of the side of the triangle Dear Dr. Math, An equilateral triangle and a circle have the same center. The area of that part of the triangle not inside the circle equals the area of that part of the circle not inside the triangle. If the radius of the circle is 1, find the length of a side of the triangle (to the nearest tenth of a unit.) Thanks for your help. Nancy Geldermann Date: 7/8/96 at 22:41:0 From: Doctor Pete Subject: Re: Find the length of the side of the triangle Call the area inside the triangle not inside the circle area A, and the area inside the circle not in the triangle area B. In addition, call the area inside both the triangle *and* the circle area C. Since A+C is the area of the triangle, and B+C is the area of the circle, it follows that if A = B, then A+C = B+C, or the area of the triangle must be equal to the area of the circle. It follows that since the area of the circle is Pi(1)^2 = Pi, the area of the triangle is also Pi. Since the triangle is equilateral, its area in terms of a single side is (Sqrt[3]x^2)/2 where x is a side. Thus Sqrt[3]x^2 = 2 Pi, or [ 2 Pi ] x = Sqrt [ ------- ] , or about 1.9046256. [ Sqrt[3] ] -Doctor Pete, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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