2006 Romanian NMO Problems/Grade 8/Problem 3
Problem
Let be a cube and a variable point on the side . The perpendicular plane on which passes through intersects the line in . Let and be the midpoints of the segments and respectively.
a) Prove that the lines and are perpendicular if and only if is the midpoint of .
b) Find the minimal value of the angle between the lines and .
Solution
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