MathDB

perpendiculars form $A, B$ and $C$ on $(EF), (FD)$ and $(DE)$ are concurrent

Source: Moldova TST 1999

August 7, 2023

geometry

Problem Statement

Outside the triangle

ABC

the isosceles triangles

AFB, BDC

and

CEA

with the bases

AB, BC

and

CA

respectively, are constructed. Show that the perpendiculars form

A, B

and

C

(EF), (FD)

and

(DE)

, respectively, are concurrent.