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Diagonals BD,CE concurrent with diameter AO in cyclic ABCDE

Source: Romanian TST 2002

February 5, 2011
symmetrytrigonometrygeometry proposedgeometry

Problem Statement

Let ABCDEABCDE be a cyclic pentagon inscribed in a circle of centre OO which has angles ∠B=120∘,∠C=120∘,\angle B=120^{\circ},\angle C=120^{\circ}, ∠D=130∘,∠E=100∘\angle D=130^{\circ},\angle E=100^{\circ}. Show that the diagonals BDBD and CECE meet at a point belonging to the diameter AOAO.
Dinu Șerbănescu
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