Question

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

Answer 1

Correct Answer - 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))`