MathDB

Given a triangle

ABC

of incenter

I

, let

P

be the intersection of the external bisector of angle

A

and the circumcircle of

ABC

, and

J

the second intersection of

PI

and the circumcircle of

ABC

. Show that the circumcircles of triangles

JIB

and

JIC

are respectively tangent to

IC

and

IB

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