2020 CIME II Problems/Problem 1
Problem
Let be a triangle. The bisector of intersects at , and the bisector of intersects at . If , , and , then the perimeter of can be expressed in the form , where and are relatively prime positive integers. Find .
Solution
For simplicity, let and . By the angle bisector theorem, we have that using as the bisected angle. Using as the bisected angle, we have that These two equations form a system of equations: Therefore, the perimeter is \ ~bhargavakanakapura
See also
2020 CIME II (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All CIME Problems and Solutions |
The problems on this page are copyrighted by the MAC's Christmas Mathematics Competitions.