Difference between revisions of "2020 CIME II Problems/Problem 1"
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| − | + | ==Problem== | |
| + | Let <math>ABC</math> be a triangle. The bisector of <math>\angle ABC</math> intersects <math>\overline{AC}</math> at <math>E</math>, and the bisector of <math>\angle ACB</math> intersects <math>\overline{AB}</math> at <math>F</math>. If <math>BF=1</math>, <math>CE=2</math>, and <math>BC=3</math>, then the perimeter of <math>\triangle ABC</math> can be expressed in the form <math>\tfrac mn</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>. | ||
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| + | ==Solution== | ||
| + | |||
| + | ==See also== | ||
| + | {{CIME box|year=2020|n=II|before=First Problem|num-a=2}} | ||
| + | |||
| + | [[Category:Introductory Geometry Problems]] | ||
| + | {{MAC Notice}} | ||
Revision as of 22:26, 5 September 2020
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
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. 
