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Turkey NMO 2000 Problem 5, Circles Have a Common Point

Source: Turkey NMO 2000 Problem 5

September 29, 2011

geometry proposedgeometry

Problem Statement

A positive real number

a

and two rays wich intersect at point

A

are given. Show that all the circles which pass through

A

and intersect these rays at points

B

and

C

where

|AB|+|AC|=a

have a common point other than

A