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

2007 iTest Problems/Problem 60

Revision as of 02:56, 8 October 2014 by Timneh (talk | contribs) (Created page with "== Problem == Let <math>T=\text{TNFTPP}</math>. Triangle <math>ABC</math> has <math>AB=6T-3</math> and <math>AC=7T+1</math>. Point <math>D</math> is on <math>BC</math> so that <...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Let $T=\text{TNFTPP}$. Triangle $ABC$ has $AB=6T-3$ and $AC=7T+1$. Point $D$ is on $BC$ so that $AD$ bisects angle $BAC$. The circle through $A, B$, and $D$ has center $O_1$ and intersects line $AC$ again at $B'$, and likewise the circle through $A, C$, and $D$ has center $O_2$ and intersects line $AB$ again at $C'$. If the four points $B', C', O_1$, and $O_2$ lie on a circle, find the length of $BC$.

Solution

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2007_iTest_Problems/Problem_60&oldid=64637"