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Find the coordinates of the circumcentre...

Find the coordinates of the circumcentre of the triangle whose vertices are `(8,6),(8-2)` and `(2,-2)` Also, find its circum-radius.

Text Solution

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. Let A(8,6), B(8,-2) and C(2,-2) be the vertices of the given triangle and let P(x,y) be the circumcentre of this triangle. Then
PA=PB=PC
⇒`PA^2=PB^2=PC^2` ⇒`(x−8)^2+(y−6)^2=(x−8)^2+(y+2)^2`
⇒`x^2+y^2−16x−12y+100=x^2+y^2−16x+4y+68`
⇒`16y=32`
⇒`y=2`
...
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Knowledge Check

  • Find the coordinates of the circum centre of the triangle whose vertices are (8,6) , (8,-2) and (2,-2) :

    A
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  • Find the coordinates of the orthocenter of the triangle whose vertices are (1, 2), (2, 3) and (4, 3)

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