Home
Class 12
MATHS
Find the coordinates of the circumcenter...

Find the coordinates of the circumcenter of the triangle whose vertices are `(A(5,-1),B(-1,5),` and `C(6,6)dot` Find its radius also.

Text Solution

Verified by Experts


Let the circumcenter be `O(x,y)`. Then
`(OA)^2=(OB)^2=(OC)^2=("Radius")^2=R^2" "(1)`
or `(x-5)^2+(y+1)^2=(x+1)^2+(y-5)^2`
`=(x-6)^2+(y-6)^2`
Taking first two relations, we get
` (x-5)^2+(y+1)^2=(x+1) ^2+(y-5)^2`
or `x=y " "(2)`
Taking last two relations, we get
`(x+1)^2+(y-5)^2=(x-6)^2+(y-6)^2`
or `(x+1)^2+(x-5)^2=(x-6)^2+(x-6)^2` [From (2)]
or `2x^28x+26=2x^-24x+72`
or `x=(23)/(8)`
or Circumcenter `-=(23//8,23//8)`
or `R^2=(x-5)^2+(y+1)^2=(OA)^2`
` =[(23)/(8)-5]^2+[(23)/(8)+1]^2`
`=(17^2)/(64)+(31^2)/(64)=(1250)/(64)`
or Radius `=(25sqrt2)/(8)"units"`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the coordinates of circumcentre of a triangle whose vertices are (-3, 1), (0, -2) and (1, 3)

Find the coordinates of centroid of a triangle whose vertices are(3-5), (4,3),(11,-4).

The orthocentre of the triangle whose vertices are (5,-2), (-1, 2) and (1,4) is

Find the centroid of the triangle whose vertices are (-5,-5), (1,-4) and (-4,-2).

Find the area of the triangle whose vertices are (3,8) ,(-4,2) and ( 5,1 )

Find the centroid of the triangle whose vertices are (2,-5),(5,11) and (9,9).

Find the direction cosines of the sides of the triangle whose vertices are (3,5,-4), (-1,1,2) and (-5,-5,-2).

Find the area of the triangle whose vertices are A (3,-1,2), B(1,-1,-3) and C(4,-3,1).

Find the coordinates of centroid of the triangle with vertices: (1, -1), (0, 6) and (-3, 0)