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Orthocentre and centroid of a triangle a...

Orthocentre and centroid of a triangle are A(-3,5) and B(3,3) respectively. If C is the circumcentre and AC is the diameter of this circle, then find the radius of the circle.

A

`sqrt10`

B

`2sqrt10`

C

`3sqrt((5)/(2))`

D

`(3sqrt5)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Key idea Orthocentre and cirucumcentre are collinear and centroid divide orthocentre and circumcentre in `2 : 1` ratio.
We have othocentre and centroid of a triangle be A(-3, 5) and B(3, 3) respectively and C circumcentre.

Clearly , AB `=sqrt((3+3)^(2)+(3-5)^(2))=sqrt(36+4)=2sqrt10`
We know that, AB : BC = 2 : 1
`rArrBC = sqrt10`
`Now, AC = AB + BC = 2sqrt10+sqrt10=3sqrt10`
Since, AC is a diameter of circle
`r = (AC)/(2)`
`rArr r = (3sqrt10)/(2)=3sqrt((5)/(2))`
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