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
We have that
But , so
Note: If it is hard to understand why , you can use the fact that the area of a triangle equals . If angle , we have that . - SuperJJ
Video Solution
CHECK OUT Video Solution: https://youtu.be/VXyOJWcpi00
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 Since we have Thus and Finally, after some calculations.
~ Nafer
~ LaTeX changes by tkfun
See also
2005 AMC 10A (Problems • Answer Key • Resources) | ||
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