2005 AMC 10A Problems/Problem 25
Contents
Problem
In we have
,
, and
. Points
and
are on
and
respectively, with
and
. What is the ratio of the area of triangle
to the area of the quadrilateral
?
Solution 1(no trig)
We have that
But , so
Solution 2(no trig)
We can let .
Since
,
.
So,
.
This means that
.
Thus,
-Conantwiz2023
Solution 3(trig)
Using this formula:
Since the area of is equal to the area of
minus the area of
,
.
Therefore, the desired ratio is
Note: was not used in this problem
Solution 4
Let be on
such that
then we have
See also
2005 AMC 10A (Problems • Answer Key • Resources) | ||
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