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max area of triangle, tangent line 2017 BMT Individual 13

Source:

January 3, 2022
geometryareasgeometric inequalitytangentarea of a triangle

Problem Statement

Two points are located 1010 units apart, and a circle is drawn with radius r r centered at one of the points. A tangent line to the circle is drawn from the other point. What value of r r maximizes the area of the triangle formed by the two points and the point of tangency?
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