If S is the circumcentre of △ABC, where A=(1,3),B=(−3,5),C=(5,−1), then
A
coordinates of S will be (−8,−10)
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B
coordinates of S will be (−4,−5)
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C
radius of circumcircle will be 5√10 units
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D
radius of circumcircle will be 5√5 units
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Solution
The correct option is C radius of circumcircle will be 5√10 units Ler S(x,y) be the circumcentre of △ABC.
We know SA=SB=SC ⇒SA2=SB2=SC2 ⇒(x−1)2+(y−3)2=(x+3)2+(y−5)2=(x−5)2+(y+1)2 ⇒−2x−6y+10=6x−10y+34=−10x+2y+26 ⇒8x−4y+24=0.........(1) 16x−12y+8=0............(2)
solving (1) and (2), we get x=−8,y=−10 ∴S≡(−8,−10)
Now radius of circumcircle will be equal to SA=SB=SC=R SA=√81+169=√250=5√10 units