MathDB

\triangle ABC

\angle C = 90^\circ, AC = 6

and

BC = 8

. Points

D

and

E

are on

\overline{AB}

and

\overline{BC}

, respectively, and

\angle BED = 90^\circ

. If

DE = 4

, then

BD =

[asy] size(100); pathpen = linewidth(0.7); pointpen = black+linewidth(3); pair A = (0,0), C = (6,0), B = (6,8), D = (2*A+B)/3, E = (2*C+B)/3; D(D("A",A,SW)--D("B",B,NW)--D("C",C,SE)--cycle); D(D("D",D,NW)--D("E",E,plain.E)); D(rightanglemark(D,E,B,16)); D(rightanglemark(A,C,B,16));[/asy]

\mathbf{(A)}\;5\qquad \mathbf{(B)}\;\frac{16}{3}\qquad \mathbf{(C)}\; \frac{20}{3}\qquad \mathbf{(D)}\; \frac{15}{2}\qquad \mathbf{(E)}\; 8

Problem Statement