IMO 1976 LL CZS7

Let P be a fixed point and T a given triangle that contains the

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IMO 1976 LL CZS7

Origin: CZS

Problem

Let P be a fixed point and T a given triangle that contains the point P. Translate the triangle T by a given vector v and denote by T ′ this new triangle. Let r, R, respectively, be the radii of the smallest disks centered at P that contain the triangles T , T ′, respectively. Prove that r + |v| \leq3R and find an example to show that equality can occur.