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Find the distance between orthocentre and circumcentre of the triangle with the vertex(0,0),(a,0),(0,b)

Find the distance between orthocentre and circumcentre of the triangle with the vertex(0,0),(a,0),(0,b)

Grade:9

1 Answers

Arun
25750 Points
6 years ago
Dear Student
 
When we draw it  we see that, it is a right angled triangle.
Hence its orthocentre will be at origin (0,0)
And its hypotenuse will be \sqrt(a²+b²).
And its circum centr will be at mid point of hypotenuse.
So distance from circum centre to orthocentre will be
distance between (0,0) to (a/2, b/2)
Distance = \sqrt(a²/4 + b²/4)
 = (1/2) \sqrt(a² + b²)
 
Regards
Arun(aakIITians forum expert)

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