Let the algebraic sum of the perpendicular distances from the points A(2, 0), B(0, 2), C(1, 1) to a variable line be zero. Then, all such lines

Let the variable line be ax + by + c = 0                           (1)Given, 2a+c+(2b+c)+(a+b+c)a2+b2+c2=0⇒ 3a + 3b + 3c = 0 or a + b + c = 0.So, the equation of the line becomesax + by – a – b = 0or, a (x – 1) + b (y – 1) = 0.⇒ the line passes through the point of intersection of linesx – 1 = 0 and y – 1 = 0, i.e., the fixed point (1, 1).So, all such lines are concurrent. Also, (1, 1) is the centroidof the ΔABC.