2006 iTest Problems/Problem 30
Contents
[hide]Problem
Triangle is equilateral. Points and are the midpoints of segments and respectively. is the point on segment such that . Let denote the intersection of and , The value of can be expressed as where and are relatively prime positive integers. Find .
Solutions
Solution 1
Since and , by SAS Similarity, . From the similarity, and .
Thus, , so .
Solution 2 (credit to jeffisepic)
Since is the midpoint of , . By SAS Congruency, , so .
By the Angle Bisector Theorem, . We know that , so . Thus, .
See Also
2006 iTest (Problems, Answer Key) | ||
Preceded by: Problem 29 |
Followed by: Problem 31 | |
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