Mock AIME 5 2005-2006 Problems/Problem 14

Problem

Let $ABC$ be a triangle such that $AB = 68$ , $BC = 100$ , and $CA = 112$ . Let $H$ be the orthocenter of $\triangle ABC$ (intersection of the altitudes). Let $D$ be the midpoint of $BC$ , $E$ be the midpoint of $CA$ , and $F$ be the midpoint of $AB$ . Points $X$ , $Y$ , and $Z$ are constructed on $HD$ , $HE$ , and $HF$ , respectively, such that $D$ is the midpoint of $XH$ , $E$ is the midpoint of $YH$ , and $F$ is the midpoint of $ZH$ . Find $AX+BY+CZ$ .

Mock AIME 5 2005-2006 (Problems, Source)
Preceded by Problem 13	Followed by Problem 15
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15

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Mock AIME 5 2005-2006 Problems/Problem 14

Contents

Problem

Solution

Solution

See also