In the diagram below, △ABC and △CDE are two right-angled triangles
with AC = 24, CE =7 and ∠ ACB = ∠ CED. Find the length of the line
segment AE.
The above is the diagram.
I came across this question in a Math Olympiad Competition. I am able to find out that △ABC and △CDE are similar triangles but after that, I am not sure what to do to solve the question. Can anyone help me with the solution? Thanks.
Best Answer
You don't even have to bother with similarity here (yes they are similar, but it doesn't matter).
Let $\angle ACB = \angle CED = \theta$. That means that $\angle ECD = 90^{\circ} - \theta$ by the angle sum of $\triangle CDE$.
That means that $\triangle ACE$ is a right triangle allowing to to apply Pythagoras' Theorem to it. So $AE = \sqrt{AC^2 + CE^2}=25$.