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Angle in Circle

Source: 2004 IrMO Paper 2 Problem 2

December 28, 2017
geometry

Problem Statement

AA and BB are distinct points on a circle TT. CC is a point distinct from BB such that ∣AB∣=∣AC∣|AB|=|AC|, and such that BCBC is tangent to TT at BB. Suppose that the bisector of ∠ABC\angle ABC meets ACAC at a point DD inside TT. Show that ∠ABC>72∘\angle ABC>72^\circ.
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