Straight Lines and Pair of Straight Lines Part 1

Let O be the centre of the circumcircle.And T be the mid-point of PR.
Since OT is perpendicular bisector of PR.
So, equation of OT is given as 2x−y+2=0
Let S be the mid-point of PQ.
Now, S will be
(‌

−2+4

2

,‌

4−2

2

)=(1,1)
and OS will be perpendicular bisector of PQ.
Equation of OS⇒‌

y−1

x−1

=‌

−1

mPQ

∵mPQ=‌

−2−4

4+2

=−1
∴ Equation of OS=y−1=1(x−1)
⇒‌‌y=x
Now, coordinates of O will be the intersection of lines OS and OT.
{

y=x

2x−y+2=0.

⇒‌‌2x−x+2=0⇒x=−2
∴‌‌y=−2
O=(−2,−2)