MathDB
Two cyclic pentagons with incenter condition implies concurrency

Source: Abelkonkurransen Finale 2024, Problem 4b

March 8, 2024
geometryincentergeometry proposedCyclicpentagon

Problem Statement

The pentagons P1P2P3P4P5P_1P_2P_3P_4P_5 andI1I2I3I4I5I_1I_2I_3I_4I_5 are cyclic, where IiI_i is the incentre of the triangle Pi−1PiPi+1P_{i-1}P_iP_{i+1} (reckoned cyclically, that is P0=P5P_0=P_5 and P6=P1P_6=P_1). Show that the lines P1I1,P2I2,P3I3,P4I4P_1I_1, P_2I_2, P_3I_3, P_4I_4 and P5I5P_5I_5 meet in a single point.
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