Posted by **james** on Sunday, December 11, 2011 at 7:20pm.

B is the midpoint of AC, D is the midpoint of CE, and Bd=14. find AE.

B is the midpoint of AC, D is the midpoint of CE and BD=7. Find AE.

- geometry -
**Steve**, Monday, December 12, 2011 at 6:10pm
Just lay out the points on the line

BD contains the right half of BC and the left half of CE

So, what's left is the same length: The left half of AC and the right half of CE

AE = AB + BC + CD + DE

but BD = BC + CD = 14

so,

AE = AB + 14 + DE

However,

AB = BC and CD = DE so AB+DE = BC+CD = 14

AE = 14 + 14 = 28

With that in hand, the 2nd problem should be trivial.

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