Consider the following diagram:

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

Shinigami Jul 11, 2022

#2**0 **

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?

BuilderBoi Jul 12, 2022