MathDB
Angle Bisector

Source:

March 21, 2006
ratiogeometryangle bisector

Problem Statement

The sides of triangle BACBAC are in the ratio 2:3:42: 3: 4. BDBD is the angle-bisector drawn to the shortest side ACAC, dividing it into segments ADAD and CDCD. If the length of ACAC is 1010, then the length of the longer segment of ACAC is: (A) 312(B) 5(C) 557(D) 6(E) 712\text{(A)} \ 3\frac12 \qquad \text{(B)} \ 5 \qquad \text{(C)} \ 5\frac57 \qquad \text{(D)} \ 6 \qquad \text{(E)} \ 7\frac12