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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