Let O(a, b) be the center of the circle. OA2=(a−1)2+(b−2)2 OB2=(a−3)2+(b+4)2 OC2=(a−5)2+(b+6)2 OD2=(a−11)2+(b+8)2 Since OA = OB = OC = OD Equating OA2=OB2
(a−1)2+(b−2)2=(a−3)2+(b+4)2
⇒4a=12b+20 a=3b+5 → (1) Equating OC2=OD2
(a−5)2+(b+6)2=(a−11)2+(b+8)2
⇒12a=4b+124 3a=b+31→ (2) From (1) and (2), Solving for a and b We get a=11 and b=2 Hence the center of the circle is (11, 2)