MathDB
Locus

Source: Iranian National Olympiad (3rd Round) 2006

September 21, 2006
geometrygeometry proposed

Problem Statement

Circle Ω(O,R)\Omega(O,R) and its chord ABAB is given. Suppose CC is midpoint of arc ABAB. XX is an arbitrary point on the cirlce. Perpendicular from BB to CXCX intersects circle again in DD. Perpendicular from CC to DXDX intersects circle again in EE. We draw three lines ℓ1,ℓ2,ℓ3\ell_{1},\ell_{2},\ell_{3} from A,B,EA,B,E parralell to OX,OD,OCOX,OD,OC. Prove that these lines are concurrent and find locus of concurrncy point.
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