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Difference between revisions of "1972 AHSME Problems/Problem 18"

(3 \frac{2}{3})
 
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==Problem==
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Let <math>ABCD</math> be a trapezoid with the measure of base <math>AB</math> twice that of base <math>DC</math>, and let <math>E</math> be the point of intersection of the diagonals. If the measure of diagonal <math>AC</math> is <math>11</math>, then that of segment <math>EC</math> is equal to
  
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<math>\textbf{(A) }3\textstyle\frac{2}{3}\qquad \textbf{(B) }3\frac{3}{4}\qquad \textbf{(C) }4\qquad \textbf{(D) }3\frac{1}{2}\qquad \textbf{(E) }3</math>
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==Solution==
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<math>\fbox{E}</math>

Revision as of 22:41, 22 June 2021

Problem

Let $ABCD$ be a trapezoid with the measure of base $AB$ twice that of base $DC$, and let $E$ be the point of intersection of the diagonals. If the measure of diagonal $AC$ is $11$, then that of segment $EC$ is equal to

$\textbf{(A) }3\textstyle\frac{2}{3}\qquad \textbf{(B) }3\frac{3}{4}\qquad \textbf{(C) }4\qquad \textbf{(D) }3\frac{1}{2}\qquad \textbf{(E) }3$

Solution

$\fbox{E}$

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