Let C₁ be a circle passing through the points A(5,1) and B(1,5) , such that its centre lies on the line 3x - y = 6 . Let C₂ be another circle passing through the points P(6,2) and Q(2,6) , such that its centre lies on the circle C₁ . If the area of the circle C₂ is strictly greater than 15 , then the square of the radius of C₂ is equal to

Step-by-step solution

The centre of C₁ lies on the perpendicular bisector of AB . The midpoint of AB is (3,3) and the slope of AB is -1 . The perpendicular bisector has slope 1 and its equation is y - 3 = 1(x - 3) y = x . The centre of C₁ is the intersection of y = x and 3x - y = 6 . 3x - x = 6 2x = 6 x = 3 . The centre of C₁ is (3,3) . The square of the radius of C₁ is (5-3)^2 + (1-3)^2 = 8 . The equation of C₁ is (x-3)^2 + (y-3)^2 = 8 . The centre of C₂ lies on the perpendicular bisector of PQ . The midpoint of PQ is (4,4) and the slo