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A tringle formed by 3 lines is tangent to the incircle

Source: IMOC 2021 G11

August 11, 2021
geometryincircletangent circlescircumcircle

Problem Statement

The incircle of △ABC\triangle ABC tangents BCBC, CACA, ABAB at DD, EE, FF, respectively. The projections of BB, CC to ADAD are UU, VV, respectively; the projections of CC, AA to BEBE are WW, XX, respectively; and the projections of AA, BB to CFCF are YY, ZZ, respectively. Show that the circumcircle of the triangle formed by UXUX, VYVY, WZWZ is tangent to the incircle of △ABC\triangle ABC.
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