Home
Class 12
MATHS
If the orthocentre and centroid of a tri...

If the orthocentre and centroid of a triangle are (-3, 5) and (3, 3) then its circumcentre 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))`
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Numerical value|12 Videos

  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

  • CROSS PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.2|13 Videos

Similar Questions

Explore conceptually related problems

The coordinates of the vertices of a triangle are (0,0) , (5,3) and (3,5) respectively , find the circumcentre and circumradius of the triangle .

If a vertex, the circumcenter, and the centroid of a triangle are (0, 0), (3,4), and (6, 8), respectively, then the triangle must be (a) a right-angled triangle (b) an equilateral triangle (c) an isosceles triangle (d) a right-angled isosceles triangle

The coordinate of the vertices B and C of the triangle ABC are (5,2,8) and (2, -3, 4) respectively, if the coordinates of the centroid of the triangle are (3, -1,3), then the coordinates of the vertex A are-

The co-ordinates of the middle points of the sides of a triangle are (4, 2), (3, 2) and (2, 2) then co-ordinates of centroid are :

The coordinates of two vertices of a triangle are (-2,3) and (5,-1) . If the orthocentre of the triangle is at the origin , find the coordinates of its third vertex.

If two vertices of a triangle are (0,2) and (4,3) and its orthocentre is (0,0) then the third vertex of the triangle lies in

Orthocentre of the triangle whose vertices are (0,0) (3,4) and (4,0) is-

The co-ordinate of three vertices and centroid of a triangle are (x, 2, 3), (3, y, 5), (-1, 6, z) and (1,4,1/3). Find x, y, z

Statement 1: If in a triangle, orthocentre, circumcentre and centroid are rational points, then its vertices must also be rational points. Statement : 2 If the vertices of a triangle are rational points, then the centroid, circumcentre and orthocentre are also rational points.

If two vertices of a triangle are (-2,3) and (5,-1) the orthocentre lies at the origin, and the centroid on the line x+y=7 , then the third vertex lies at