KEAM 2015 Math Paper

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=2√5