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Mathley 2014.3 p5 by Tran Quang Hung

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August 18, 2020
incirclegeometryconcurrent

Problem Statement

Triangle ABCABC has incircle (I)(I) and P,QP,Q are two points in the plane of the triangle. Let QA,QB,QCQA,QB,QC meet BA,CA,ABBA,CA,AB respectively at D,E,FD,E,F. The tangent at DD, other than BCBC, of the circle (I)(I) meets PAPA at XX. The points YY and ZZ are defined in the same manner. The tangent at XX, other than XDXD, of the circle (I)(I) meets (I) (I) at UU. The points V,WV,W are defined in the same way. Prove that three lines (AU,BV,CW)(AU,BV,CW) are concurrent.
Tran Quang Hung, Dean of the Faculty of Science, Thanh Xuan, Hanoi.
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