Points inside a triangle are 'related' algebraically to points at the vertices. We introduce the idea using a problem from I.S.I. B.Stat 2014.
Problem: Let $PQR$ be a triangle. Take a point $A$ on or inside the triangle. Let $f(x, y) = ax + by + c$. Show that f(A)≤max f(P),f(Q),f(R)
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