MathDB
2021 Team #9

Source:

June 27, 2021
geometrycircumcircleincenter

Problem Statement

Let scalene triangle ABCABC have circumcenter OO and incenter II. Its incircle ω\omega is tangent to sides BC,CA,BC,CA, and ABAB at D,E,D,E, and FF, respectively. Let PP be the foot of the altitude from DD to EFEF, and let line DPDP intersect ω\omega again at Q≠DQ \ne D. The line OIOI intersects the altitude from AA toBC BC at TT. Given that OI∥BC,OI \|BC, show that PQ=PTPQ=PT.
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