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circle with every point on intersection of 2 planes

Source: Polish MO Finals 1981 p1

August 24, 2024
geometry3D geometry

Problem Statement

Two intersecting lines aa and bb are given in a plane. Consider all pairs of orthogonal planes α\alpha, β\beta such that a⊂αa \subset \alpha and b⊂βb\subset \beta. Prove that there is a circle such that every its point lies on the line α∩β\alpha \cap \beta for some α\alpha and β\beta.
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