since, the lines x+y=6 and x+2y=4 are two diameters of the circle, then their point of intersection will be the centre of circle. Put y=6−x in x+2y=4, we get x+2(6−x)=4⇒x+12−2x=4⇒−x=−8⇒x=8⇒y=6−8=−2 Hence, centre of the circle is (8,−2) . Radius of circle = Distance between (8,−2) and (6,2)=(8−6)2+(−2−2)2​=4+16​=20​=25​