MathDB

16

Part of 1997 IMO Shortlist

Problems(1)

Collinear iff the points P, Q, and O are collinear

Source: IMO Shortlist 1997, Q16

8/10/2008
In an acute-angled triangle ABC, ABC, let AD,BE AD,BE be altitudes and AP,BQ AP,BQ internal bisectors. Denote by I I and O O the incenter and the circumcentre of the triangle, respectively. Prove that the points D,E, D, E, and I I are collinear if and only if the points P,Q, P, Q, and O O are collinear.
geometryincentercircumcircletrigonometryangle bisectorcollinearityIMO Shortlist