1965 AHSME Problems/Problem 36

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Problem

Given distinct straight lines $OA$ and $OB$. From a point in $OA$ a perpendicular is drawn to $OB$; from the foot of this perpendicular a line is drawn perpendicular to $OA$. From the foot of this second perpendicular a line is drawn perpendicular to $OB$; and so on indefinitely. The lengths of the first and second perpendiculars are $a$ and $b$, respectively. Then the sum of the lengths of the perpendiculars approaches a limit as the number of perpendiculars grows beyond all bounds. This limit is:

$\textbf{(A)}\ \frac {b}{a - b} \qquad  \textbf{(B) }\ \frac {a}{a - b} \qquad  \textbf{(C) }\ \frac {ab}{a - b} \qquad  \textbf{(D) }\ \frac{b^2}{a-b}\qquad \textbf{(E) }\ \frac{a^2}{a-b}$

Solution

$\fbox{E}$

See Also

1965 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 35
Followed by
Problem 37
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