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

2012 MPFG Problem 10

Revision as of 01:13, 26 August 2025 by Cassphe (talk | contribs) (Created page with "==Problem== Let <math>\Delta ABC</math> be a triangle with a right angle <math>\angle ABC</math>. Let <math>D</math> be the midpoint of <math>BC</math>, let <math>E</math> be...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Let $\Delta ABC$ be a triangle with a right angle $\angle ABC$. Let $D$ be the midpoint of $BC$, let $E$ be the midpoint of $AC$, and let $F$ be the midpoint of $AB$. Let $G$ be the midpoint of $EC$. One of the angles of $\Delta DFG$ is a right angle. What is the least possible value of $\frac{BC}{AG}$ ? Express your answer as a fraction in simplest form.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2012_MPFG_Problem_10&oldid=258921"