Problem 281

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Problem 281: (2003 AMC 12b,22)

Let $ABCD$ be a rhombus with $AC = 16$ and $BD = 30$. Let $N$ be a point on $\overline{AB}$, and let $P$ and $Q$ be the feet of the perpendiculars from $N$ to $\overline{AC}$ and $\overline{BD}$, respectively. Which of the following is closest to the minimum possible value of $PQ$?

$\mathrm{(A)}\ 6.5 \qquad$ $\mathrm{(B)}\ 6.75 \qquad$ $\mathrm{(C)}\ 7 \qquad$ $\mathrm{(D)}\ 7.25 \qquad$ $\mathrm{(E)}\ 7.5$

Solution

Exercise 281: Solution

Let $ABCD$ be a rhombus with $AC = 30$ and $BD = 40$. Let $N$ be a point on $\overline{AB}$, and let $P$ and $Q$ be the feet of the perpendiculars from $N$ to $\overline{AC}$ and $\overline{BD}$, respectively. What is the minimum possible value of $PQ$?

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