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for any choice of P the points D_P , E_P and F are collinear

Source: 2022 Austrian Federal Competition For Advanced Students, Part 2 p5

October 5, 2022

collineargeometryisosceles

Problem Statement

Let

ABC

be an isosceles triangle with base

AB

. We choose a point

P

inside the triangle on altitude through

C

. The circle with diameter

CP

intersects the straight line through

B

and

P

again at the point

D_P

and the Straight through

A

and

C

one more time at point

E_P

. Prove that there is a point

F

such that for any choice of

P

the points

D_P , E_P

and

F

lie on a straight line.
(Walther Janous)