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Let the orthocentre and centroid of a triangle be `(-3,5) and B(3,3)` respectively. If C is the circumcentre of the triangle then the radrus of the circle having line segment AC as diameter, is

A

`(3sqrt5)/(2)`

B

`sqrt10`

C

`2sqrt10`

D

`3sqrt(5)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
In a triangle orthocenter A centriod B and circumcentre C are always collinear such that `AB:BC=2:1`

So, slope of AD is infinity.
Let orthocenter have coordinates (2,k).
Slope of AC is `-2`.
`therefore Slope of BH,(k-2)/(2-5)=(1)/(2)`
`therefore k=(1)/(2)`
`therefore AC=sqrt((6-(-3))^2+(2-5)^2)=sqrt(81+9)=sqrt90=3sqrt10`
AC is diameter of the circle.
`therefore`"Radius of circle" `=(3)/(2)sqrt10=3sqrt(5/(2))`
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