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>.
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<asy>
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draw((3,4)--(0,0)--(9,0)--(3,4)--(6,0));
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dot((0,0));
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dot((9,0));
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dot((3,4));
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dot((6,0));
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label("A", (0,0), W);
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label("B", (3,4), N);
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label("C", (9,0), E);
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label("D", (6,0), S);</asy>
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<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>
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== Solution ==
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== See also ==
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{{AHSME box|year=1989|num-b=14|num-a=16}} 
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[[Category: Introductory Geometry Problems]]
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 06:53, 22 October 2014

Problem

In $\triangle ABC$, $AB=5$, $BC=7$, $AC=9$, and $D$ is on $\overline{AC}$ with $BD=5$. Find the ratio of $AD:DC$.

[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]

$\textrm{(A)}\ 4:3\qquad\textrm{(B)}\ 7:5\qquad\textrm{(C)}\ 11:6\qquad\textrm{(D)}\ 13:5\qquad\textrm{(E)}\ 19:8$

Solution

See also

1989 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 14
Followed by
Problem 16
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