MathDB

Five points

O,A,B,C,D

are taken in order on a straight line with distances

OA=a

OB=b

OC=c

, and

OD=d

P

is a point on the line between

B

and

C

and such that

AP:PD=BP:PC

. Then

OP

equals:

\text{(A)}\ \dfrac{b^2-bc}{a-b+c-d} \qquad \text{(B)}\ \dfrac{ac-b}{a-b+c-d} \qquad \text{(C)}\ -\dfrac{bd+c}{a-b+c-d}\qquad\\ \text{(D)}\ \dfrac{bc+ad}{a+b+c+d}\qquad \text{(E)}\ \dfrac{ac-bd}{a+b+c+d} \qquad

Problem Statement