2006 iTest Problems/Problem 32
Problem
Triangle is scalene. Points and are on segment with between and such that , , and . If and trisect , then can be written uniquely as , where and are relatively prime positive integers and is a positive integer not divisible by the square of any prime. Determine .
Solution
Let and . Since , by the Angle Bisector Theorem, we have and .
By using the Law of Cosines on and , we have
By using the Law of Cosines on and , we have
Multiplying the second equation by and adding the two equations results in
After substituting back, solve for to get
Thus, , so .
NOTE: SIMPLY USE STEWARTS THEOREM
See Also
2006 iTest (Problems, Answer Key) | ||
Preceded by: Problem 31 |
Followed by: Problem 33 | |
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