Mission2012 wrote:What is the greatest possible area of a triangular region with one vertex at the center of a circle of radius 1 and the other two vertices on the circle?
(A) √3/4
(B) 12
(C) 4Ï€
(D) 1
(E)√2
The drawings above show 3 different versions of the triangle.
Leftmost drawing: b=1, h=1.
Middle drawing: b=1, h<1.
Rightmost drawing: b=1, h<1.
Notice that in each triangle b=1, but only in the leftmost triangle does h=1. In the other two triangles, h<1, resulting in a smaller area. The drawings above illustrate the following rule:
Given two sides of a triangle, the greatest area will be achieved when a right angle is placed between them (as in the leftmost triangle).
Thus, the greatest possible area = 1/2 * 1 * 1 = 1/2.
The correct answer is
B.
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