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A rod AB of length 2a is situated on coordinate axis then locus of the circumcentre triangle OAB.

A rod AB of length 2a is situated on coordinate axis then locus of the circumcentre triangle OAB.

Grade:11

1 Answers

Harshit
31 Points
6 years ago
Let the rod lies on the x-axis at (u,0) and y-axis at (0,v) and the coordinate of circumcentre is (h,k) where u,v,h,k are variables.
Triangle OAB is a right angle triangle so circumcentre will lie on the mid point of the hypotenuse. Then the coordinate of circumcentre is
( u/2 ,v/2 ) on comparing
u/2=h   v/2=k
u=2h   v=2k
 
by Pythagoras's theorem
u2+v2=(2a)2
(2h)2+(2k)2=(2a)2
h2+k2=a2
x2+y2=a2 is the locus of circumcenter

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