MathDB

2

Part of 1984 National High School Mathematics League

Problems(2)

Choose the figure

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

2/22/2020
Which figure's shaded part satisfies the inequality log⁡x(log⁡xy2)>0\log_x(\log_x y^2)>0? https://services.artofproblemsolving.com/download.php?id=YXR0YWNobWVudHMvNi83LzY2ZWE5OGJmZjlhNzI1NDM5ZjdiNjZmYTcyZTFkMzEzZjUzMzk5LnBuZw==&rn=NGRkLnBuZw==
inequalities
Skew Lines

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

2/22/2020
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|.