### IMO Shortlist 1994 problem G5

Kvaliteta:

Avg: 0,0Težina:

Avg: 8,0 A circle with center and a line which does not touch circle is perpendicular to is on is on draw two tangents to circle are perpendicular to respectively. ( on on ). Prove that, line intersect at a fixed point.

Original formulation:

A line does not meet a circle with center is the point on such that is perpendicular to is any point on other than The tangents from to touch it at and is the point on such that is perpendicular to is the point on such that is perpendicular to The line cuts at Prove that the location of is independent of that of

Original formulation:

A line does not meet a circle with center is the point on such that is perpendicular to is any point on other than The tangents from to touch it at and is the point on such that is perpendicular to is the point on such that is perpendicular to The line cuts at Prove that the location of is independent of that of

Izvor: Međunarodna matematička olimpijada, shortlist 1994