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3D Geometry Problem

Source: 1988 National High School Mathematics League, Exam One, Problem 4

February 25, 2020
geometry3D geometry

Problem Statement

Given three planes α,β,γ\alpha,\beta,\gamma. Intersection angle between any two planes are all θ\theta.α∩β=a,β∩γ=b,γ∩α=c\alpha\cap\beta=a,\beta\cap\gamma=b,\gamma\cap\alpha=c. Given two conditions: A: θ>π3\theta>\frac{\pi}{3} B: a,b,ca,b,c share one point. (A)(\text{A})A is sufficient but unnecessary condition of B. (B)(\text{B})A is necessary but insufficient condition of B. (C)(\text{C})A is sufficient and necessary condition of B. (D)(\text{D})None above
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