Question

Let ABC be a triangle. Let X be on the segment BC such that AB = AX. Let A meet the circumcircle Γ of triangle ABC again at D. Show that the circumcentre of ΔBDX lies on Γ.

Answer 1

Draw AP ⊥ BX

∴ 'P' is circumcentre of ΔBDX which is lying on circumcircle of ΔABC.