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11

Part of 2004 Iran MO (3rd Round)

Problems(1)

nice one

Source: iran2004(geo exam)

9/10/2004
assume that ABC is acute traingle and AA' is median we extend it until it meets circumcircle at A". let APaAP_a be a diameter of the circumcircle. the pependicular from A' to APaAP_a meets the tangent to circumcircle at A" in the point XaX_a; we define Xb,XcX_b,X_c similary . prove that Xa,Xb,XcX_a,X_b,X_c are one a line.
geometrycircumcircleprojective geometrymodular arithmeticEulergeometry proposed