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 "2023 SSMO Team Round Problems/Problem 3"

(Created page with "==Problem== Let <math>ABC</math> be a triangle such that <math>AB=4\sqrt{2}, BC=5\sqrt{2},</math> and <math>AC=\sqrt{82}.</math> Let <math>\omega</math> be the circumcircle of...")
 
(→‎Solution)
Line 3: Line 3:
  
 
==Solution==
 
==Solution==
 +
 +
Note that <math>\Delta{ABC}</math> is right, meaning that <math>\overline{\rmQWE}</math>

Revision as of 01:52, 3 January 2024

Problem

Let $ABC$ be a triangle such that $AB=4\sqrt{2}, BC=5\sqrt{2},$ and $AC=\sqrt{82}.$ Let $\omega$ be the circumcircle of $\triangle ABC$. Let $D$ be on the circle such that $\overline{BD} \perp \overline{AC}.$ Let $E$ be the point diametrically opposite of $B$. Let $F$ be the point diametrically opposite $D$. Find the area of the quadrilateral $ADEF$ in terms of a mixed number $a\frac{b}{c}$. Find $a+b+c$.

Solution

Note that $\Delta{ABC}$ is right, meaning that $\overline{\rmQWE}$ (Error compiling LaTeX. Unknown error_msg)

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2023_SSMO_Team_Round_Problems/Problem_3&oldid=209670"