As shown in the diagram, one end of a -foot-long electric cable is fixed at point A on the wall, and the other end of the cable (denoted by C) is a sensor. There is a pin attached to the cable at a point B that is 4 units away from C, and the pin can be fixed to any point on the wall reachable by B. Due to gravity, the free part of the cable (i.e. BC) is always perpendicular to the ground OD. A few other measurements are provided in the diagram. What is the minimum distance between C and D?
(Apparently this is the latex?)
[asy]
size(6cm);
pair A,B,C,D,O;
A=(0,9);
D=(12,0);
B=(5,5);
C=(5,1);
draw(A--O^^O--D,dashed);
draw(A..(A+B)/2+(0,-1)..B--C);
draw(rightanglemark(D,O,A,20));
dot(Label("$A$",A,N));
dot(Label("$B$",B,N));
dot(Label("$C$",C,W));
dot(Label("$D$",D,E));
dot(Label("$O$",O,S));
label("9 feet",A--O,W);
label("12 feet", D--O,S);
label("4 feet",B--C,E) ;
[/asy]
+364 \([asy] size(6cm); pair A,B,C,D,O; A=(0,9); D=(12,0); B=(5,5); C=(5,1); draw(A--O^^O--D,dashed); draw(A..(A+B)/2+(0,-1)..B--C); draw(rightanglemark(D,O,A,20)); dot(Label("A",A,N)); dot(Label("B",B,N)); dot(Label("C",C,W)); dot(Label("D",D,E)); dot(Label("O",O,S)); label("9 feet",A--O,W); label("12 feet", D--O,S); label("4 feet",B--C,E) ; [/asy]\)doesn't work
Here you go!
!
