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A triangle are (6,0).(0, 6) and (6,6). I...

A triangle are` (6,0).(0, 6)` and `(6,6)`. If distance between circumcenter and orthocenter and distance between circumcenter and centroid are `lambda` and `u` unit respectively, then `(lambda, u)` lies on:

A

`y=3x`

B

`x=3y`

C

`y=2x`

D

`x=2y`

Text Solution

Verified by Experts

The correct Answer is:
C
Clearly, triangle with vertices A (6,0) ,B(0,6) and C(6,6) is a right-triangled right angled at C. So, the coordinates of its orthocentre are (6,6) and the circumcentre is the mid-point of hypotenus. AB. Thus, the coordinates of the circumcentre are (3,3) .
Hence, required distance `=sqrt((6-3)^(2)+(6-3)^(2))=3sqrt(2)`
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