# geometry

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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 -

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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