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

Options

A. `(3sqrt5)/(2)`
B. `sqrt10`
C. `2sqrt10`
D. `3sqrt(5)/(2)`

Answer

D

Explanation

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))`