Let, C (x, y, z) be the centre of sphere AC = BC = CC' = CD = r CO=√x2+(y−5)2+z2 AO=√(x−4)2+(y−3)2+z2 DO=√(x−4)2+y2+(z−3)2 BO=√x2+(y−4)2+(z−3)2 CO=AO x2+(y−5)2+z2=(x−4)2+(y−3)2+z2 ⇒x2+y2−10y+25=x2−8x+16+y2−6y+9 ⇒8x−4y=0 ⇒2x=y.....(1) Now, DO=BO (x−4)2+(y)2+(z−3)2=(x)2+(y−4)2+(z−3)2 ⇒x2−8x+16+y2=x2+y2−8y+16 ⇒8x−8y=0 ⇒x=y.....(2) From (1) and (2), 2x=x⇒x=0So,y=0 AO=DO 16+9+z2=16+z2−6z+9 ⇒ 6z=0 ⇒ z = 0 ∴ Radius =CO=√(0+(5)2+0) = 5 units Hence, option (1) is correct.