question_answer

Let the orthocentre and centroid of a triangle be A(-3, 5) and B(3, 3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter,  is:   [JEE Main Online 08-04-2018]

A)  \[3\sqrt{\frac{5}{2}}\]                      

B)  \[\frac{3\sqrt{5}}{2}\]

C)  \[\sqrt{10}\]               

D)  \[2\sqrt{10}\]

Correct Answer: A

Solution :

                \[AC=\frac{3}{2}AB=\frac{3}{2}\sqrt{{{6}^{2}}+{{2}^{2}}}=3\sqrt{10}\] \[\Rightarrow r=\frac{3}{2}\sqrt{10}=3\sqrt{\frac{5}{2}}\]