1993 AMC 12 #27 - Rolling Circle inside Triangle
Source:
January 2, 2012
geometryperimetertrigonometryratioAMC
Problem Statement
The sides of have lengths and . A circle with center and radius rolls around the inside of , always remaining tangent to at least one side of the triangle. When first returns to its original position, through what distance has traveled?
[asy]
draw((0,0)--(8,0)--(8,6)--(0,0));
draw(Circle((4.5,1),1));
draw((4.5,2.5)..(5.55,2.05)..(6,1), EndArrow);
dot((0,0));
dot((8,0));
dot((8,6));
dot((4.5,1));
label("A", (0,0), SW);
label("B", (8,0), SE);
label("C", (8,6), NE);
label("8", (4,0), S);
label("6", (8,3), E);
label("10", (4,3), NW);
label("P", (4.5,1), NW);
[/asy]