Exam

JEE Main

Year

2018

Date

8 April

Subject

Mathematics

Chapter

Properties of Triangles

JEE Main 2018 · 8 April · Mathematics · Properties of Triangles

Let the orthocentre and centroid of a triangle be A(- 3, 5) and...

Let the orthocentre and centroid of a triangle be $A\left(- 3, 5\right)$ and $B\left(3, 3\right)$ respectively. If $C$ is the circumcentre of this triangle, then the radius of the circle having line segment $AC$ as diameter, is:

Step-by-step solution

Centroid $B$ divides the line joining Orthocentre $A$ and circumcentre $C$ in the ratio $2: 1$

$AB = \sqrt{{\left(3 + 3\right)}^{2} + {\left(5 - 3\right)}^{2}} = \sqrt{{6}^{2} + {2}^{2}} = \sqrt{40} = 2\sqrt{10}$

$AC = \dfrac{3}{2} \times 2\sqrt{10} = 3\sqrt{10}$

Radius $= \dfrac{AC}{2} = 3\sqrt{\dfrac{10}{4}} = 3\sqrt{\dfrac{5}{2}}$