MathDB

49

Part of 1990 IMO Longlists

Problems(1)

The projection of T on OG - ILL 1990 LUX1

Source:

9/19/2010
AB,ACAB, AC are two chords of the circle centered at OO. The diameter, which is perpendicular to BCBC, intersects AB,ACAB, AC at F,GF, G respectively (FF is in the circle). The tangent from GG tangents the circle at TT. Prove that FF is the projection of TT on OG.OG.
geometry proposedgeometry