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If the vertices of triangles are placed at (0,0), (0,6), (6,0). The prove that the distance between the orthocentre and circumcentre is 3 root2.

If the vertices of triangles are placed at (0,0), (0,6), (6,0). The prove that the distance between the orthocentre and circumcentre is 3 root2.

Grade:12

1 Answers

Ajay Verma
askIITians Faculty 33 Points
6 years ago
Solution:
As we know the.. orthocentre is the point of intersection of altitudes of the triangle...
soo for right angle triangle.. orthocenter is the vertex itself on which right angle is made..
Circumcentre : circumcentre is the poin of intersection of the perpendicular bisector of the sides of the triangle..
so for rightangle triangle... circumcentre is the midpoint of the hypotenuse..


203-746_07.png

so distance b/w Orhtocentre and Circumcentre is
OD = (32+ 32)1/2
= 3*(2)1/2



thanks and regards

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