prove that the point (-1, 2) is the center of a circle passing through the points (-3, 11) , (5, 9), (8, 0) and (6, 8) find the radius of the circle
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Answer:
We need to check if the distance between the centre and the points on the circle is the same.
Distance between two points (x
1
,y
1
) and (x
2
,y
2
) can be calculated using the formula
(x
2
−x
1
)
2
+(y
2
−y
1
)
2
Distance between the points O (3,3) and A (4,0)=
(4−3)
2
+(0−3)
2
=
1+9
=
10
Distance between the points O (3,3) and B (6,2)=
(6−3)
2
+(2−3)
2
=
9+1
=
10
Distance between the points O (3,3) and C (4,6)=
(4−3)
2
+(6−3)
2
=
1+9
=
10
Distance between the points O (3,3) and D (0,4)=
(0−3)
2
+(4−3)
2
=
9+1
=
10
Since, length of the sides between the centre and the all the other vertices are equal.
They all lie on the circle with radius
10
.
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