Show that the circumcircle of the triangle formed by the lines ; and passes through…

MATHEMATICS · Subjective · A Level · Mathematics · Coordinate geometry in the (x y) plane · Coordinate geometry in the (x y) plane

Problem

Show that the circumcircle of the triangle formed by the lines

ax + by + c = 0

;

bx + cy + a = 0

and

cx + ay + b = 0

passes through the origin if

(b^2 + c^2)(c^2 + a^2)(a^2 + b^2) = abc(b + c)(c + a)(a + b)