This question was uploaded on 28/01/22 on social media accounts.
Solution:
We know that:
\[\color{blue} {s^2+x^2=a^2+b^2}\]
By using cosine rule:
\[\color{black} {2ab\cos(135)=a^2+b^2-2s^2}\]
\[\Rightarrow\color{red} {-\sqrt2ab=a^2+b^2-2s^2}\]
By combining both equations:
\[\color{purple} {2s^2=a^2+b^2+\sqrt2ab}\]
\[\color{green} {2r^2=a^2+b^2-\sqrt2ab}\]
From these two equations:
\[\color{fuchsia} {s^2-r^2=\sqrt2ab}\]
