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Turkey EGMO TST 2019 P5

Source: Turkey EGMO TST 2019

March 15, 2019
geometry

Problem Statement

Let DD be the midpoint of BC‾\overline{BC} in ΔABC\Delta ABC. Let PP be any point on AD‾\overline{AD}. If the internal angle bisector of ∠ABP\angle ABP and ∠ACP\angle ACP intersect at QQ. Prove that, if BQ⊥QCBQ \perp QC, then QQ lies on ADAD
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