MathDB
Fixed point

Source: Moldova TST 2006 Test II problem 2

March 25, 2006
geometrycircumcirclepower of a pointradical axisgeometry proposed

Problem Statement

Let C1C_1 be a circle inside the circle C2C_2 and let PP in the interior of C1C_1, QQ in the exterior of C2C_2. One draws variable lines lil_i through PP, not passing through QQ. Let lil_i intersect C1C_1 in Ai,BiA_i,B_i, and let the circumcircle of QAiBiQA_iB_i intersect C2C_2 in Mi,NiM_i,N_i. Show that all lines Mi,NiM_i,N_i are concurrent.
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