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Skew Lines

Source: 1984 National High School Mathematics League, Exam Two, Problem 2

February 22, 2020

Problem Statement

a,ba,b are two skew lines, the angle they form is θ\theta. Length of their common perpendicular AA′AA' is dd(A′∈a,A∈b)A'\in a,A\in b). E∈a,F∈b,∣A′E∣=m,∣AF∣=nE\in a,F\in b,|A'E|=m,|AF|=n. Calculate ∣EF∣|EF|.
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