A triangle is inscribed in a circle of radius 1. The distance between the orthocentre and the circumcentre of the triangle cannot be

Options

A. 1
B. 2
C. `(3)/(2)`
D. 4

Answer

D

Explanation

Let the verices of the triangle be `(cos theta_(i),sin theta_(i)), i=1,2,3`.
`:.` Circumcenter is (0,0)
Also orthocentre `-= (cos theta_(1)+cos theta_(2)+cos theta_(3))`,
`sin theta_(1)+sin theta_(2) + sin theta_(3))`
`rArr` Distance between the orthocentre and the circumcentre
`sqrt((cos theta_(1)+cos theta_(2)+cos theta_(3))^(2)+(sin theta_(1)+sin theta_(2)+sin theta_(3))^(2))lt3`