MathDB

Circumcircle and external bisector

Source: Iberoamerican Olympiad 2009, problem 4

September 24, 2009

geometrycircumcircleincentercyclic quadrilateralgeometry proposed

Problem Statement

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