MHB Incircle and circumscribed circle prove :d=√(R(R−2r))

[Albert1]

$\triangle ABC$ with its incircle $I$ (radius $r$)
and circumscribed circle $O$ (radius $R$)
the distance between points $O$(circumcenter) and $I$(incenter) is $d$
prove:$d=\sqrt {R(R-2r)}$

 

[Albert1]

$\triangle ABC$ with its incircle $I$ (radius $r$)
and circumscribed circle $O$ (radius $R$)
the distance between points $O$(circumcenter) and $I$(incenter) is $d$
prove:$d=\sqrt {R(R-2r)}$

Spoiler

$d=\sqrt{R^2-2Rr}$
View attachment 6507