2016 AMC 12B Problems/Problem 17
Problem
In shown in the figure,
,
,
, and
is an altitude. Points
and
lie on sides
and
, respectively, so that
and
are angle bisectors, intersecting
at
and
, respectively. What is
?
Solution
Get the area of the triangle by heron's formula:
Use the area to find the height AH with known base BC:
Apply angle bisector theorem on triangle
and triangle
, we get
and
, respectively.
To find AP, PH, AQ, and QH, apply variables, such that
is
and
is
. Solving them out, you will get
,
,
, and
. Then, since
according to the Segment Addition Postulate, and thus manipulating, you get
\frac{7\sqrt{5}}{3}
\frac{9\sqrt{5}}{5}$ =
See Also
2016 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 16 |
Followed by Problem 18 |
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All AMC 12 Problems and Solutions |
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