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Prove that S4 is similar to S - ISL 1977

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September 20, 2010
geometryconvex quadrilateralperpendicularIMO Shortlist

Problem Statement

Let SS be a convex quadrilateral ABCDABCD and OO a point inside it. The feet of the perpendiculars from OO to AB,BC,CD,DAAB, BC, CD, DA are A1,B1,C1,D1A_1, B_1, C_1, D_1 respectively. The feet of the perpendiculars from OO to the sides of SiS_i, the quadrilateral AiBiCiDiA_iB_iC_iD_i, are Ai+1Bi+1Ci+1Di+1A_{i+1}B_{i+1}C_{i+1}D_{i+1}, where i=1,2,3.i = 1, 2, 3. Prove that S4S_4 is similar to S.
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