MathDB

Let

ABC

be an acute angled triangle with

AC>AB

and incircle

\omega

. Let

\omega

touch the sides

BC, CA,

and

AB

D, E,

and

F

respectively. Let

X

and

Y

be points outside

\triangle ABC

satisfying

\angle BDX = \angle XEA = \angle YDC = \angle AFY = 45^{\circ}.

Prove that the circumcircles of

\triangle AXY, \triangle AEF

and

\triangle ABC

meet at a point

Z\ne A

.
Proposed by Atul Shatavart Nadig and Shantanu Nene

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