MathDB
2016 Team #10

Source:

December 30, 2016
incirclecollinearity

Problem Statement

Let ABCABC be a triangle with incenter II whose incircle is tangent to BC‾\overline{BC}, CA‾\overline{CA}, AB‾\overline{AB} at DD, EE, FF. Point PP lies on EF‾\overline{EF} such that DP‾⊥EF‾\overline{DP} \perp \overline{EF}. Ray BPBP meets AC‾\overline{AC} at YY and ray CPCP meets AB‾\overline{AB} at ZZ. Point QQ is selected on the circumcircle of △AYZ\triangle AYZ so that AQ‾⊥BC‾\overline{AQ} \perp \overline{BC}.
Prove that PP, II, QQ are collinear.
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