1990 AHSME Problems/Problem 20

Problem

$[asy] pair A = (0,0), B = (7,4.2), C = (10, 0), D = (3, -5), E = (3, 0), F = (7,0); draw(A--B--C--D--cycle,dot); draw(A--E--F--C,dot); draw(D--E--F--B,dot); markscalefactor = 0.1; draw(rightanglemark(B, A, D)); draw(rightanglemark(D, E, C)); draw(rightanglemark(B, F, A)); draw(rightanglemark(D, C, B)); MP("A",(0,0),W); MP("B",(7,4.2),N); MP("C",(10,0),E); MP("D",(3,-5),S); MP("E",(3,0),N); MP("F",(7,0),S); [/asy]$

In the figure $ABCD$ is a quadrilateral with right angles at $A$ and $C$ . Points $E$ and $F$ are on $\overline{AC}$ , and $\overline{DE}$ and $\overline{BF}$ are perpendicual to $\overline{AC}$ . If $AE=3, DE=5,$ and $CE=7$ , then $BF=$

$\text{(A) } 3.6\quad \text{(B) } 4\quad \text{(C) } 4.2\quad \text{(D) } 4.5\quad \text{(E) } 5$

Solution

$\fbox{C}$

1990 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 19	Followed by Problem 21
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1990 AHSME Problems/Problem 20

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