2009 AMC 12B Problems/Problem 16
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Problem
Trapezoid has
,
,
, and
. The ratio
is
. What is
?
Solution
Solution 1
Extend and
to meet at
. Then
Thus is isosceles with
. Because
, it follows that the triangles
and
are similar. Therefore
so
Solution 2
Let be the intersection of
and the line through
parallel to
By constuction
and
; it follows that
is the bisector of the angle
. So by the Angle Bisector Theorem we get
The answer is
.
See also
2009 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 15 |
Followed by Problem 17 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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