MathDB

fixed point for lines

Source: VI Soros Olympiad 1990-00 R2 10.5 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 28, 2024

geometryfixedFixed point

Problem Statement

Two different points

A

and

B

have been marked on the circle

\omega

. We consider all points

X

of the circle

\omega

, different from

A

and

B

. Let

Y

be the middpoint of the chord

AX

and

Z

be the projection of point

A

on the line

BX

. Prove that all straight lines

YZ

pass through a certain fixed point that does not depend on the choice of point

X