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ratio of angles in cylic quad

Source: (2021-) 2022 XV 15th Dürer Math Competition Finals Day 2 E+5

December 12, 2022
ratiogeometryangles

Problem Statement

On a circle kk, we marked four points (A,B,C,D)(A, B, C, D) and drew pairwise their connecting segments. We denoted angles as seen on the diagram. We know that α1:α2=2:5\alpha_1 : \alpha_2 = 2 : 5, β1:β2=7:11\beta_1 : \beta_2 = 7 : 11, and γ1:γ2=10:3\gamma_1 : \gamma_2 = 10 : 3. If δ1:δ2=p:q\delta_1 : \delta_2 = p : q, where pp and qq are coprime positive integers, then what is pp? https://cdn.artofproblemsolving.com/attachments/c/e/b532dd164a7cf99cea7b3b7d98f81796622da5.png
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