Consider the following triangle:
As shown in the picture, the circum-radius of triangle $ABC$ is $R$ and its in-radius is $r$. How can we use trigonometric identities to prove that the value of $d$ is given by $$d=\sqrt{R^2 - 2Rr} ,$$ using the angles at the three vertices at the triangle (angles $A, B$ and $C$ respectively)?
I'm aware that there is a famous proof of this (known as Euler's Theorem in geometry), but I came across this question while going through a chapter about the properties of a triangle, where it is specifically mentioned in the question that we must consider the angles at the respective vertices as $A, B$ and $C$. This made me think that it should be solved using trigonometry. I can't think of how I can get started. Any hints/working will be appreciated, thanks in advance!