1983 AHSME Problems/Problem 19
Problem
Point is on side of triangle . If , then the length of is
Solution
Let . Since bisects , the Angle Bisector Theorem gives , so let and . Applying the Law of Cosines to gives , and to gives . Subtracting times the first equation from the second equation therefore yields , so is or . But since ( is the length of a side of a triangle), must be , so the answer is .
See Also
1983 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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