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MathNet 2017-part-05 — 176 problems (EN–VI) Question 9

Math Olympiad Vault · MathNet 2017-part-05 — 176 problems (EN–VI)

Question 9

Let $ABCDA'B'C'D'$, be a cube with side length $a$. Let $M$ and $P$ be the midpoints of the edges $[AB]$ and $[DD']$, respectively.
a) Prove that $MP \perp A'C$.
b) Find the distance between the lines $MP$ and $A'C$.