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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_________

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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"`.
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