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three circle

Source: Iranian 3rd round Geometry exam P1

September 25, 2014
geometrycircumcirclegeometry proposed

Problem Statement

In the circumcircle of triange △ABC,\triangle ABC, AA′AA' is a diameter. We draw lines l′l' and ll from A′A' parallel with Internal and external bisector of the vertex AA. l′l' Cut out AB,BCAB , BC at B1B_1 and B2B_2. ll Cut out AC,BCAC , BC at C1C_1 and C2C_2. Prove that the circumcircles of △ABC\triangle ABC △CC1C2\triangle CC_1C_2 and △BB1B2\triangle BB_1B_2 have a common point.
(20 points)
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