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Iran TST 2021 First Exam,P1

Source: Iran TST 2021

May 16, 2021

geometrytangent

Problem Statement

In acute scalene triangle

ABC

the external angle bisector of

\angle BAC

meet

BC

at point

X

.Lines

l_b

and

l_c

which tangents of

B

and

C

with respect to

(ABC)

.The line pass through

X

intersects

l_b

and

l_c

at points

Y

and

Z

respectively. Suppose

(AYB)\cap(AZC)=N

and

l_b\cap l_c=D

. Show that

ND

is angle bisector of

\angle YNZ

. Proposed by Alireza Haghi

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