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Let ABCDE be a convex pentagon whose vertices lie on a circle

Source: 2024 5th OMpD L3 P2 - Brazil - Olimpíada Matemáticos por Diversão

October 16, 2024
geometry

Problem Statement

Let ABCDE ABCDE be a convex pentagon whose vertices lie on a circle Γ \Gamma . The tangents to Γ \Gamma at C C and E E intersect at X X , and the segments CE CE and AD AD intersect at Y Y . Given that CE CE is perpendicular to BD BD , that XY XY is parallel to BD BD , that AY=BD AY = BD , and that ∠BAD=30∘ \angle BAD = 30^\circ , what is the measure of the angle ∠BDA \angle BDA ?
Proposed by João Gilberti Alves Tavares
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