MathDB

Concurrency wanted, perpendiculars to a line given

Source: Turkey TST 2021 P3 Day 1

March 13, 2022

geometryconcurrencyincenter

Problem Statement

In a triangle

ABC

, the incircle centered at

I

is tangent to the sides

BC, AC

and

AB

D, E

and

F

, respectively. Let

X, Y

and

Z

be the feet of the perpendiculars drawn from

A, B

and

C

to a line

\ell

passing through

I

. Prove that

DX, EY

and

FZ

are concurrent.