MathDB

Incenter of small triangle lies on incircle

Source: KoMaL A. 885

October 11, 2024

geometryincenterAngle-chasing

Problem Statement

Let triangle

ABC

be a given acute scalene triangle with altitudes

AB

and

CF

. Let

\triangle CDF

be the point where the incircle of

\,\triangle ABC

touches side

BC

. The circumcircle of

\triangle BDE

meets line

AB

again at point

K

, the circumcircle of

\triangle CDF

meets line

AC

again at point

L

. The circumcircle of

\triangle BDE

and

\triangle CDF

meet line

KL

again at

X

and

Y

, respectively. Prove that the incenter of

\triangle DXY

lies on the incircle of

\,\triangle ABC

.
Proposed by Luu Dong, Vietnam

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