MathDB

The diagram below shows

\vartriangle ABC

with point

D

on side

\overline{BC}

. Three lines parallel to side

\overline{BC}

divide segment

\overline{AD}

into four equal segments. In the triangle, the ratio of the area of the shaded region to the area of the unshaded region is

\frac{49}{33}

and

\frac{BD}{CD} = \frac{m}{n}

, where

m

and

n

are relatively prime positive integers. Find

m + n

. https://cdn.artofproblemsolving.com/attachments/2/8/77239633b68f073f4193aa75cdfb9238461cae.png

Problem Statement