MathDB

Let

ABC

be a triangle and let

A' \in BC

B' \in CA

and

C' \in AB

be three collinear points. a) Prove that each pair of circles of diameters

AA'

BB'

and

CC'

has the same radical axis; b) Prove that the circumcenter of the triangle formed by the intersections of the lines

AA' , BB'

and

CC'

lies on the common radical axis found above.

Problem Statement