MathDB

Common point as a varies

Source: Problem 2, Polish NO 1994

October 7, 2005

conicsgeometrytrapezoidprojective geometrygeometry solved

Problem Statement

Let be given two parallel lines

k

and

l

, and a circle not intersecting

k

. Consider a variable point

A

on the line

k

. The two tangents from this point

A

to the circle intersect the line

l

at

B

and

C

. Let

m

be the line through the point

A

and the midpoint of the segment

BC

. Prove that all the lines

m

(as

A

varies) have a common point.

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