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2017 IGO Advanced P4

Source: 4th Iranian Geometry Olympiad (Advanced) P4

September 15, 2017

IGOIrangeometry

Problem Statement

Three circles

\omega_1,\omega_2,\omega_3

are tangent to line

l

at points

A,B,C

(

B

lies between

A,C

) and

\omega_2

is externally tangent to the other two. Let

X,Y

be the intersection points of

\omega_2

with the other common external tangent of

\omega_1,\omega_3

. The perpendicular line through

B

to

l

meets

\omega_2

again at

Z

. Prove that the circle with diameter

AC

touches

ZX,ZY

.
Proposed by Iman Maghsoudi - Siamak Ahmadpour

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