If the vertices of a triangle are at `O(0, 0), A (a, 0) and B (0, b)`. Then, the distance between its circumcentre and orthocentre is

Options

A. `sqrt(a^(2)+b^(2))`
B. `(1)/(2)sqrt(a^(2)+b^(2))`
C. `sqrt((a^(2)+b^(2))/(2))`
D. `(1)/(4)sqrt(a^(2)+b^(2))`

Answer

B

Explanation

Clearly, `DeltaOAB` is a right triangle in right angled at O.
So, its orthocentre is at O(0,0) and circumcentre is the mid-point of irts hypotenus i.e., `((a)/(2),(b)/(2))`
`:.` Required distance = `sqrt(((a)/(2)-0)^(2)+((b)/(2)-0)^(2))=(1)/(2)sqrt(a^(2)+b^(2))`