Difference between revisions of "1990 AHSME Problems/Problem 20"
(Created page with "== Problem == In the figure <math>ABCD</math> is a quadrilateral with right angles at <math>A</math> and <math>C</math>. Points <math>E</math> and <math>F</math> are on <math>\o...") |
m (→Problem) |
||
Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
+ | <asy> | ||
+ | draw((0,0)--(7,4.2)--(10,0)--(3,-5)--cycle,dot); | ||
+ | draw((0,0)--(3,0)--(7,0)--(10,0),dot); | ||
+ | draw((3,-5)--(3,0)--(7,0)--(7,4.2),dot); | ||
+ | draw((3/sqrt(34),-5/sqrt(34))--(3/sqrt(34)+1/sqrt(1.36),-5/sqrt(34)+.6/sqrt(1.36))--(1/sqrt(1.36),.6/sqrt(1.36)),black+linewidth(.5)); | ||
+ | draw((10-7/sqrt(74),0-5/sqrt(74))--(10-7/sqrt(74)-5/sqrt(74),0-5/sqrt(74)+7/sqrt(74))--(10-5/sqrt(74),7/sqrt(74)),black+linewidth(.5)); | ||
+ | draw((3,-1)--(4,-1)--(4,0),black+linewidth(.5)); | ||
+ | draw((6,0)--(6,1)--(7,1),black+linewidth(.5)); | ||
+ | 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 <math>ABCD</math> is a quadrilateral with right angles at <math>A</math> and <math>C</math>. Points <math>E</math> and <math>F</math> are on <math>\overline{AC}</math>, and <math>\overline{DE}</math> and <math>\overline{BF}</math> are perpendicual to <math>\overline{AC}</math>. If <math>AE=3, DE=5, </math> and <math>CE=7</math>, then <math>BF=</math> | In the figure <math>ABCD</math> is a quadrilateral with right angles at <math>A</math> and <math>C</math>. Points <math>E</math> and <math>F</math> are on <math>\overline{AC}</math>, and <math>\overline{DE}</math> and <math>\overline{BF}</math> are perpendicual to <math>\overline{AC}</math>. If <math>AE=3, DE=5, </math> and <math>CE=7</math>, then <math>BF=</math> |
Revision as of 01:13, 30 September 2014
Problem
In the figure is a quadrilateral with right angles at
and
. Points
and
are on
, and
and
are perpendicual to
. If
and
, then
Solution
See also
1990 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.