MathDB

collinear wanted, toucpoints of incircle related

Source: 2018 Thailand October Camp 1.2

October 15, 2020

geometryincirclecollinear

Problem Statement

Let

\Omega

be the inscribed circle of a triangle

\vartriangle ABC

. Let

D, E

and

\Omega

be the tangency points of

K, L

and the sides

BC, CA

and

AB

, respectively, and let

AD, BE

and

CF

intersect

\Omega

at

K, L

and

M

, respectively, such that

D, E, F, K, L

and

Y

are all distinct. The tangent line of

\Omega

at

DF

intersects

EF

at

X

, the tangent line of

\Omega

at

L

intersects

DE

at

Y

, and the tangent line of

\Omega

at M intersects

DF

at

Z

. Prove that

X,Y

and

Z

are collinear.

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