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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.

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Draw AP ⊥ BX

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

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