Difference between revisions of "1984 AIME Problems/Problem 3"
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== Problem == | == Problem == | ||
+ | A point <math>P</math> is chosen in the interior of <math>\triangle ABC</math> such that when lines are drawn through <math>P</math> parallel to the sides of <math>\triangle ABC</math>, the resulting smaller triangles <math>t_{1}</math>, <math>t_{2}</math>, and <math>t_{3}</math> in the figure, have areas <math>4</math>, <math>9</math>, and <math>49</math>, respectively. Find the area of <math>\triangle ABC</math>. | ||
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== Solution == | == Solution == | ||
{{solution}} | {{solution}} |
Revision as of 23:39, 20 January 2007
Problem
A point is chosen in the interior of
such that when lines are drawn through
parallel to the sides of
, the resulting smaller triangles
,
, and
in the figure, have areas
,
, and
, respectively. Find the area of
.
Solution
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