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Geometry with Spiral Similarity from Turkey TST

Source: 2023 Turkey D3 P9

March 29, 2023

geometry

Problem Statement

The points

A,B,K,L,X

lies of the circle

\Gamma

in that order such that the arcs

\widehat{BK}

and

\widehat{KL}

are equal. The circle that passes through

A

and tangent to

BK

at

B

intersects the line segment

KX

at

P

and

Q

. The circle that passes through

A

and tangent to

BL

at

B

intersect the line segment

BX

for the second time at

T

. Prove that

\angle{PTB} = \angle{XTQ}

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