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# Help and thank you in advance!

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Consider the following diagram:

Then what are the lengths of AE and CE equal to, in that order?

Jul 11, 2022

#1
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AE = 5*sqrt(2), CE = 3*sqrt(3)

Jul 11, 2022
#2
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Let $$AE= x$$ and $$CE = y$$

From $$\triangle AEC$$, we have the equation: $$x^2 + y^2 = 81$$

Using the Pythagorean Theorem on $$\triangle CAD$$ and $$\triangle DAB$$, we find that $$DB = 12 \sqrt {2}$$

Also, from $$\triangle BEC$$, we have the equation: $$(x+7)^2 + y^2 = (12 \sqrt 2)^2$$

Now we just need to solve the system for x and y.

Can you take it from here?

Jul 12, 2022