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Find the distance between orthocenter and Circumcenter of the triangle of the triangle With the vertices (0,0),(a,0),and (0,b)

Find the distance between orthocenter and Circumcenter of the triangle of the triangle With the vertices (0,0),(a,0),and (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(askIITians forum expert)

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