Finding the Length of a Partial Chord
Source:
March 8, 2009
Problem Statement
In a circle with center , is a diameter, is a chord, BO \equal{} 5, and . Then the length of is:[asy]size(200);
defaultpen(linewidth(0.7)+fontsize(10));
pair O=origin, A=dir(35), C=dir(155), D=dir(215), B=intersectionpoint(dir(125)--O, A--C);
draw(C--A--D^^B--O^^Circle(O,1));
pair point=O;
label("", A, dir(point--A));
label("", B, dir(point--B));
label("", C, dir(point--C));
label("", D, dir(point--D));
label("", O, dir(305));label("", B--O, dir(O--B)*dir(90));
label("", dir(185), dir(185));
label("", B+0.05*dir(-25), dir(-25));[/asy] (A)\ 3 \qquad (B)\ 3 \plus{} \sqrt3 \qquad (C)\ 5 \minus{} \frac{\sqrt3}{2} \qquad (D)\ 5 \qquad (E)\ \text{none of the above}