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Extending the sides of a circumscribed quadrilateral

Source: Question 3 - Brazilian Mathematical Olympiad 2017

December 7, 2017
geometrycircumscribed quadrilateralincircleincenterBrazilian Math OlympiadBrazilian Math Olympiad 2017

Problem Statement

3. A quadrilateral ABCDABCD has the incircle ω\omega and is such that the semi-lines ABAB and DCDC intersect at point PP and the semi-lines ADAD and BCBC intersect at point QQ. The lines ACAC and PQPQ intersect at point RR. Let TT be the point of ω\omega closest from line PQPQ. Prove that the line RTRT passes through the incenter of triangle PQCPQC.
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