1964 AHSME Problems/Problem 39
Problem
The magnitudes of the sides of triangle are , , and , as shown, with . Through interior point and the vertices , , , lines are drawn meeting the opposite sides in , , , respectively. Let . Then, for all positions of point , is less than:
Solution
We know that in a , if then , we can use this fact in the different triangles to form inequalities, and then add the inequalities.
In , since , we have by the above argument.
Now, , hence we have
And, , hence we have
And, , hence we have
Finally, adding all three inequalities, we have
See Also
1964 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 38 |
Followed by Problem 40 | |
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