MathDB
Easy nonagon geo

Source: 44th International Tournament of Towns, Junior A-Level P5, Fall 2022

February 16, 2023
geometrynonagonTournament of Towns

Problem Statement

On the sides of a regular nonagon ABCDEFGHIABCDEFGHI, triangles XAB,YBC,ZCDXAB, YBC, ZCD and TDETDE are constructed outside the nonagon. The angles at X,Y,Z,TX, Y, Z, T in these triangles are each 20∘20^\circ. The angles XAB,YBC,ZCDXAB, YBC, ZCD and TDETDE are such that (except for the first angle) each angle is 20∘20^\circ greater than the one listed before it. Prove that the points X,Y,Z,TX, Y , Z, T lie on the same circle.
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