Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2017 AIME II Problems/Problem 10"

(Created page with "<math>\textbf{Problem 10}</math> Rectangle <math>ABCD</math> has side lengths <math>AB=84</math> and <math>AD=42</math>. Point <math>M</math> is the midpoint of <math>\overlin...")
 
Line 1: Line 1:
−
<math>\textbf{Problem 10}</math>
+
==Problem==
 
Rectangle <math>ABCD</math> has side lengths <math>AB=84</math> and <math>AD=42</math>. Point <math>M</math> is the midpoint of <math>\overline{AD}</math>, point <math>N</math> is the trisection point of <math>\overline{AB}</math> closer to <math>A</math>, and point <math>O</math> is the intersection of <math>\overline{CM}</math> and <math>\overline{DN}</math>. Point <math>P</math> lies on the quadrilateral <math>BCON</math>, and <math>\overline{BP}</math> bisects the area of <math>BCON</math>. Find the area of <math>\triangle CDP</math>.
 
Rectangle <math>ABCD</math> has side lengths <math>AB=84</math> and <math>AD=42</math>. Point <math>M</math> is the midpoint of <math>\overline{AD}</math>, point <math>N</math> is the trisection point of <math>\overline{AB}</math> closer to <math>A</math>, and point <math>O</math> is the intersection of <math>\overline{CM}</math> and <math>\overline{DN}</math>. Point <math>P</math> lies on the quadrilateral <math>BCON</math>, and <math>\overline{BP}</math> bisects the area of <math>BCON</math>. Find the area of <math>\triangle CDP</math>.
  
−
<math>\textbf{Problem 10 Solution}</math>
+
==Solution==
 
<math>\boxed{546}</math>
 
<math>\boxed{546}</math>
 +
 +
=See Also=
 +
{{AIME box|year=2017|n=II|num-b=9|num-a=11}}
 +
{{MAA Notice}}

Revision as of 12:55, 23 March 2017

Problem

Rectangle $ABCD$ has side lengths $AB=84$ and $AD=42$. Point $M$ is the midpoint of $\overline{AD}$, point $N$ is the trisection point of $\overline{AB}$ closer to $A$, and point $O$ is the intersection of $\overline{CM}$ and $\overline{DN}$. Point $P$ lies on the quadrilateral $BCON$, and $\overline{BP}$ bisects the area of $BCON$. Find the area of $\triangle CDP$.

Solution

$\boxed{546}$

See Also

2017 AIME II (Problems • Answer Key • Resources)
Preceded by
Problem 9 		Followed by
Problem 11
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. AMC logo.png

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2017_AIME_II_Problems/Problem_10&oldid=84903"