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cyclic wanted, 3 reflections and incircle related

Source: INAMO Shortlist 2014 G1

July 13, 2019

geometrygeometric transformationreflection

Problem Statement

The inscribed circle of the

ABC

triangle has center

I

and touches to

BC

at

F

. Suppose the

D

and

BC

lines intersect at

L

, and

D

is the reflection of

L

wrt

X

. Points

E

and

F

respectively are the result of a reflection of

D

wrt to lines

CI

and

BI

respectively. Show that quadrilateral

BCEF

is cyclic .

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