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2008 ToT Spring Senior A P4 angles

Source:

February 26, 2020
geometryangles

Problem Statement

Each of Peter and Basil draws a convex quadrilateral with no parallel sides. The angles between a diagonal and the four sides of Peter's quadrilateral are α,α,β\alpha, \alpha, \beta and γ\gamma in some order. The angles between a diagonal and the four sides of Basil's quadrilateral are also α,α,β\alpha, \alpha, \beta and γ\gamma in some order. Prove that the acute angle between the diagonals of Peter's quadrilateral is equal to the acute angle between the diagonals of Basil's quadrilateral.
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