I am helping my young nephew with his math homework. There is a problem which I was unable to solve, despite having several college math courses finished. This is the problem:
There is a right angled triangle $ABC$. It has its right angle at the point $C$. By using point reflection, we create
- point $A'$ by reflecting $A$ over C
- point $B'$ by reflecting B over A
- point $C'$ by reflecitng C over B
Knowing the lengths $|AB|, |BC|, |CA|$, calculate $|A'B'|^2, |B'C'|^2, |C'A'|^2$
No goniometric functions are allowed. Just pure Pythagoras' theorem and basic triangle identities about its height, altitudes, orthocentres, etc.
I was able to solve the length $|C'A'|^2 = 4|CB|^2+|AC|^2$. I was unable to solve for the other two. How would one go about solving them?
EDIT: $ABC$ is not necessarily an isosceles triangle.
