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Source: iran2004(geo exam)

September 10, 2004
geometrycircumcircleprojective geometrymodular arithmeticEulergeometry proposed

Problem Statement

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.
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