Difference between revisions of "1989 AHSME Problems/Problem 15"
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| − | + | == Problem == | |
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| + | In <math>\triangle ABC</math>, <math>AB=5</math>, <math>BC=7</math>, <math>AC=9</math>, and <math>D</math> is on <math>\overline{AC}</math> with <math>BD=5</math>. Find the ratio of <math>AD:DC</math>. | ||
| + | |||
| + | <asy> | ||
| + | draw((3,4)--(0,0)--(9,0)--(3,4)--(6,0)); | ||
| + | dot((0,0)); | ||
| + | dot((9,0)); | ||
| + | dot((3,4)); | ||
| + | dot((6,0)); | ||
| + | label("A", (0,0), W); | ||
| + | label("B", (3,4), N); | ||
| + | label("C", (9,0), E); | ||
| + | label("D", (6,0), S);</asy> | ||
| + | |||
| + | <math> \textrm{(A)}\ 4:3\qquad\textrm{(B)}\ 7:5\qquad\textrm{(C)}\ 11:6\qquad\textrm{(D)}\ 13:5\qquad\textrm{(E)}\ 19:8 </math> | ||
| + | |||
| + | == Solution == | ||
| + | |||
| + | == See also == | ||
| + | {{AHSME box|year=1989|num-b=14|num-a=16}} | ||
| + | |||
| + | [[Category: Introductory Geometry Problems]] | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 06:53, 22 October 2014
Problem
In 
, 
, 
, 
, and 
is on 
with 
. Find the ratio of 
.
![[asy] draw((3,4)--(0,0)--(9,0)--(3,4)--(6,0)); dot((0,0)); dot((9,0)); dot((3,4)); dot((6,0)); label("A", (0,0), W); label("B", (3,4), N); label("C", (9,0), E); label("D", (6,0), S);[/asy]](http://latex.artofproblemsolving.com/c/a/2/ca2ac4d63a5b4135fad339af8a7de33bae68e881.png)
Solution
See also
| 1989 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Problem 16 | |
| 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. 
