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the distance between the circumcenter and orthocenter of the triangle whose vertices are (0,0),(6,8),(-4,3) ?

the distance between the circumcenter and orthocenter of the triangle whose vertices are (0,0),(6,8),(-4,3) ?

Grade:11

1 Answers

Arun
25750 Points
6 years ago
when we find the  side lengths of triangles
we get lengths as 10, 5, 5\sqrt5
this forms a right angled triangle
hence orthocentre will be (0, 0)             (point of intersection of base and perpendicular)
and circumcentre will be the mid point of hypotenuse i.e. mid point of (6, 8) & ( –4, 3)
hence circumcentre will be at (1, 11/2)
now the distance between circum centre and orthocentre will be
= \sqrt(1+121/4) = \sqrt125/4 = (5/2)\sqrt5
hope it helps

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