Difference between revisions of "2021 AIME I Problems/Problem 11"
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==Problem== | ==Problem== | ||
| − | + | Let <math>ABCD</math> be a cyclic quadrilateral with <math>AB=4,BC=5,CD=6,</math> and <math>DA=7</math>. Let <math>A_1</math> and <math>C_1</math> be the feet of the perpendiculars from <math>A</math> and <math>C</math>, respectively, to line <math>BD,</math> and let <math>B_1</math> and <math>D_1</math> be the feet of the perpendiculars from <math>B</math> and <math>D,</math> respectively, to line <math>AC</math>. The perimeter of <math>A_1B_1C_1D_1</math> is <math>\frac mn</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>. | |
==Solution== | ==Solution== | ||
Revision as of 16:49, 11 March 2021
Problem
Let 
be a cyclic quadrilateral with 
and 
. Let 
and 
be the feet of the perpendiculars from 
and 
, respectively, to line 
and let 
and 
be the feet of the perpendiculars from 
and 
respectively, to line 
. The perimeter of 
is 
, where 
and 
are relatively prime positive integers. Find 
.
Solution
See also
| 2021 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
