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Geometry inequality

Source: Mathematics Regional Olympiad of Mexico Southeast 2020 P5

October 23, 2021
geometrycircumcircleInequalityTangentsinequalities

Problem Statement

Let ABCABC an acute triangle with ∠BAC≥60∘\angle BAC\geq 60^\circ and Γ\Gamma it´s circumcircule. Let PP the intersection of the tangents to Γ\Gamma from BB and CC. Let Ω\Omega the circumcircle of the triangle BPCBPC. The bisector of ∠BAC\angle BAC intersect Γ\Gamma again in EE and Ω\Omega in DD, in the way that EE is between AA and DD. Prove that AEED≤2\frac{AE}{ED}\leq 2 and determine when equality holds.
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