Let (X,d) be a metric space with the added condition that for any three points x,y,z in X, d(x,y) <= max{d(x,z),d(y,z)}. (a) Show that every triangle in X is isoceles. (b) An open ball in X with center u in X and radius r > 0 is defined as B(u;r) = {x in X | d(u,x) < r}. Show that every point in an open ball is a center for the open ball.

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