Distance between Incenter and excenter

If the distance between incenter and one of the excenter of an equilateral triangle is 4 units,then find the inradius of the triangle.

Distance Between Circumcenter and incenter

If veca, vecb and vecc are position vectors of A,B, and C respectively of DeltaABC and if|veca-vecb|=4,|vecb-vec(c)|=2, |vecc-veca|=3 , then the distance between the centroid and incenter of triangleABC is

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

Incentives

Distance between two points

Distance Between A line and a points