2015 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 3
Problem
Show that the bisect of an angle in a triangle divides the opposite side in segments whose
lengths have the same ratio as the ratio of the adjacent sides,
![\[AN/NB = CA/CB\]](http://latex.artofproblemsolving.com/c/c/4/cc4046d24edd6833365b1eefa3a0fc2836a4ed97.png)
in the picture below. NOTE: The same is true for the bisector of an exterior angle of a
triangle, i.e., it divides the opposite side externally into segments that are proportional
to the adjacent sides. You do not have to write a proof of this fact.
Solution
See also
| 2015 UNM-PNM Contest II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNM-PNM Problems and Solutions | ||
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