= Metric geodesic triangle
{title2=$[p,q]\cup[q,r]\cup[r,p]$}
A metric geodesic triangle consists of three points of a <geodesic metric space> and a chosen <metric geodesic> segment between each pair. Multiple choices are allowed, and coincident vertices give degenerate triangles. A <Gromov-hyperbolic metric space> has a uniform bound on the distance from each side to the other two sides for every such choice. This definition applies to <Cayley graphs> and trees without tangent vectors or curvature assumptions; it does not invoke the surface angle formula for a <geodesic triangle>.
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