2013 Mock AIME I Problems/Problem 13

Problem

In acute $\triangle ABC$ , $H$ is the orthocenter, $G$ is the centroid, and $M$ is the midpoint of $BC$ . It is obvious that $AM \ge GM$ , but $GM \ge HM$ does not always hold. If $[ABC] = 162$ , $BC=18$ , then the value of $GM$ which produces the smallest value of $AB$ such that $GM \ge HM$ can be expressed in the form $a+b\sqrt{c}$ , for $b$ squarefree. Compute $a+b+c$ .

Solution

$\boxed{010}$ .

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2013 Mock AIME I Problems/Problem 13

Problem

Solution

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