1984 AHSME Problems/Problem 26
Contents
Problem
In the obtuse triangle with , , , and ( is on , is on , and is on ). If the area of is , then the area of is
Solution 1
We let side have length , have length , and have angle measure . We then have that
Now I shall find the lengths of and in terms of the defined variables. Note that is defined to be the midpoint of , so . We can then use trigonometric manipulation on triangle to get that . We can also use trig manipulation on to get that .
Now note that is the height of triangle originating from vertex , so we have that
However, this is simply half the area of triangle , so , which makes the correct answer.
Solution 2
It is well known that . But ~. As a result .
See Also
1984 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 25 |
Followed by Problem 27 | |
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