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Translating a triangle by a given vector

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January 3, 2011
vectorgeometry unsolvedgeometry

Problem Statement

Let PP be a fixed point and TT a given triangle that contains the point PP. Translate the triangle TT by a given vector v\bold{v} and denote by T′T' this new triangle. Let r,Rr, R, respectively, be the radii of the smallest disks centered at PP that contain the triangles T,T′T , T', respectively. Prove that r+∣v∣≤3Rr + |\bold{v}| \leq 3R and find an example to show that equality can occur.
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