MathDB

Let

ABC

be a triangle with

AC>AB

, and denote its circumcircle by

\Omega

and incentre by

I

. Let its incircle meet sides

BC,CA,AB

D,E,F

respectively. Let

X

and

Y

be two points on minor arcs

\widehat{DF}

and

\widehat{DE}

of the incircle, respectively, such that

\angle BXD = \angle DYC

. Let line

XY

meet line

BC

K

. Let

T

be the point on

\Omega

such that

KT

is tangent to

\Omega

and

T

is on the same side of line

BC

A

. Prove that lines

TD

and

AI

meet on

\Omega

.
[right]Tommy Walker Mackay, United Kingdom[/right]

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