Prove that the distance between the circumcenter and the incenter of triangle ABC is`sqrt(R^2-2R r)`

Prove that the distance between the circumcenter and the incenter of triangle ABC is sqrt(R^(2)-2Rr)

Distance Between Circumcenter and incenter

In A B C ,l e tR=c i r c u m r a d i u s ,r=in r a d i u sdot If r is the distance between the circumcenter and the incenter, the ratio R/r is equal to sqrt(2)-1 (b) sqrt(3)-1 sqrt(2)+1 (d) sqrt(3)+1

In A B C ,l e tR=c i r c u m r a d i u s ,r=in r a d i u sdot If r is the distance between the circumcenter and the incenter, the ratio R/r is equal to sqrt(2)-1 (b) sqrt(3)-1 sqrt(2)+1 (d) sqrt(3)+1

In triangle A B C ,l e tR=c i r c u m r a d i u s ,r= i n r a d i u sdot If r is the distance between the circumcenter and the incenter, the ratio R/r is equal to (a) sqrt(2)-1 (b) sqrt(3)-1 (c) sqrt(2)+1 (d) sqrt(3)+1

In triangle A B C ,l e tR=c i r c u m r a d i u s ,r= i n r a d i u sdot If r is the distance between the circumcenter and the incenter, the ratio R/r is equal to (a) sqrt(2)-1 (b) sqrt(3)-1 (c) sqrt(2)+1 (d) sqrt(3)+1

In DeltaABC , let R = circumradius, r= inradius. If r is the distance between the circumcenter and the incenter, then ratio R/r is equal to

Prove using vectors that the distance of the circumcenter of the Delta ABC form the centroid is sqrt(R^(2) - (1)/(9)(a^(2) + b^(2) + c^(2))) where R is the circumradius.

Prove that the distance of the incentre of Delta ABC from A is 4R sin B/2 sin C/2.