Question

Find the coordinates of circumvent re and radius of circumcircle of triangle ABC if A(7, 1) B(3,5) and C(2,0) are given​

Answer 1

Answer:

ANSWER

Consider the given points of a triangle

A(x

1

,y

1

)=(7,1)

B(x

2

,y

2

)=(3,5)

C(x

3

,y

3

)=(2,0)

Let O be the circumcentre

O(x,y)=(

3

x

1

+x

2

+x

3

,

3

y

1

+y

2

+y

3

)

O(x,y)=(

3

7+3+2

,

3

1+5+0

)

O(x,y)=(

3

12

,

3

6

)

O(x,y)=(4,2)

Now, radius of circumcircle

Let D(x

4

,y

4

) be the middle point of AB.

The

D(x

4

,y

4

)=(

2

x

1

+x

2

,

2

y

1

+y

2

)

D(x

4

,y

4

)=(

2

7+3

,

2

1+5

)

D(x

4

,y

4

)=(5,3)

radius of circumcircle is

=OD=

(x−x

4

)

2

+(y−y

4

)

2

OD=

(4−5)

2

+(2−3)

2

OD=

1+1

=

2