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angle wanted, arc midpoints of circumcircle, angle bisectors

Source: 239 MO 2021 8-9 p1

May 2, 2021

geometrycircumcircleanglesarc midpointangle bisector

Problem Statement

Points

X

and

Y

are the midpoints of arcs

AB

and

BC

of the circumscribed circle of triangle

ABC

. Point

T

lies on side

AC

. It turned out that the bisectors of the angles

ATB

and

BTC

pass through points

X

and

Y

respectively. What angle

B

can be in triangle

ABC