Question

Find the circumcenter of the triangle whose sides are given by x + y + 2 =0, 5x - y - 2 = 0) and
x-2y +5=0.​

Answer 1

Answer:

Find the circumcentre of △

3x−y−5=0....(i)

x+2y−4=0.....(ii)

5x+3y+1=0.....(iii)

First find the vertices of the △

Solving (i) and (ii) simultaneously

x

1

=2,y

1

=1 ∴A(2,1)

Similarly solving (ii) and (iii) simultaneously

x

2

=−2,y

2

=3

∴ B(−2,3)

Finally from (i) and (iii) x

3

=1,y

3

=−2 C(1,−2)

Let the equation of circle through A,B,C be x

2

+y

2

+2gx+2fy+c=0

put the coordinates of A(2,1)

4+1+4g+2g+c=0

4g+2f+c=−5....(iv)

Similarly by putting coordinates of B(−2,3) in the circle equation we get

4g−6g−c=13....(v)

and putting C(1,−2)

2g−4f+c=−5....(vi)

Solving (iv), (v), (vi) simultaneously

f=−

7

2

,g=

7

6

,c=−

7

5.5

The circumcentre of the circle ≡(−g,−f)

≡(−

7

6

,

7

2

)

Answer 2

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