Home
Class 12
MATHS
The distance between the circumcenter an...

The distance between the circumcenter and the orthocentre of the triangle whose vertices are `(0,0),(6,8),` and `(-4,3)` is `Ldot` Then the value of `2/(sqrt(5))L` is_________

Text Solution

Verified by Experts

The correct Answer is:
5
Given vertices of triangle are `O(0,0) ,B(6,8)`, and `C(-4,3)`,
Slope of `OB=(8)/(6)=(4)/(3)`
Slope of `OC=-(3)/(4)`
`therefore angleBOC=(pi)/(2)`
`Delta OBC` is right-angled at O.
Circumcenter = Midpoint of hypotenuse `BC=(1,(11)/(2))`
Orthocenter =Vertex `O(0,0)`
Required distance `=sqrt((1+(121)/(4)))=(5sqrt5)/(2) "units"`.
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE|Exercise JEE Main Previous Year|6 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise (Matrix)|4 Videos

  • COORDINATE SYSTEM

    CENGAGE|Exercise Multiple Correct Answers Type|2 Videos

  • CROSS PRODUCTS

    CENGAGE|Exercise DPP 2.2|13 Videos

Similar Questions

Explore conceptually related problems

The distance between the circumcenter and the orthocentre of the triangle whose vertices are (0,0),(6,8), and (-4,3) is L. Then the value of (2)/(sqrt(5))L is

Find the orthocentre of the triangle whose vertices are (0, 0), (6, 1) and (2, 3).

The distance between circum centre and orthocenter of the triangle whose vertices are (0,0),(6,8) and (-4,3) is

Find the orthocentre of the triangle whose vertices are (0,0),quad (3,0), and (0,4)

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

The orthocentre of the triangle whose vertices are (5,-2),(-1,2) and (1,4) is

The orthocentre of the triangle whose vertices are (1, 1), (5, 1) and (4, 5) is

circumcentre of the triangle whose vertices are (1,0),(3,0) and (1,6) is