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A rod PQ of length 2a slides with its end on the axes then locous of circumcenter of triangle OPQ is ?

 A rod PQ of length 2a slides with its end on the axes then locous of circumcenter of triangle OPQ is ?

Grade:12

1 Answers

Vikas TU
14149 Points
6 years ago
Given that A pole PQ of length 2a slides with its end on the tomahawks. Subsequently the pole dependably makes right calculated triangle with right point at inception. 
Let the finishes of bars ne (x,0) and (0,y) anytime of time. 
We realize that circumcenter of a privilege calculated triangle is the midpoint of hypotenuse. 
Subsequently midpoint of hypotenuse will be ( (x+0)/2 , (0+y)/2 ) = (x/2 , y/2) 
By utilizing pythogorous hypothesis 
X^2 + y^2 = 4a^2 
(x/2)^2 + (y/2)^2 = a^2 
Subsequently the locus of circumcenter of triangle OPQ is a circle 

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