SOLUTION: In triangle ABC, the angle bisector AL meets the median BM at E. EM = 200 and BE = 300, and AL divides BC into two segments of length BL = 600 and LC = x. Find the value of x.

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Question 1176504: In triangle ABC, the angle bisector AL meets the median BM at E.
EM = 200 and BE = 300, and AL divides BC into two segments of length BL = 600 and LC = x.
Find the value of x.

All I was able to do so far is draw a picture but I'm stuck. Please help? Thanks!
Found 2 solutions by mananth, math_tutor2020:
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!

You have to apply angle bisector theorem for two triangles ABM and ABC
Us the median property to substitute AM = 1/2 * AC

Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!

The tutor @manath has the correct drawing and correct final answer of x = 800

However, this is from solving the equation 300/400 = 600/x

If you solved 300/400 = 600/(600+x), then you would get x = 200 instead which is not correct.

The equation 300/400 = 600/x is due to AB/AC = BL/LC (angle bisector theorem).