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MathNet 2019-part-05 — 184 problems (EN–VI) Question 82

Math Olympiad Vault · MathNet 2019-part-05 — 184 problems (EN–VI)

Question 82

In the regular hexagonal prism $ABCDEFA_1B_1C_1D_1E_1F_1$ one constructs the points $P, Q$, the projections of the point $A$ on the lines $A_1B$, respectively $A_1C$, and $R, S$, the projections of the point $D_1$ on the lines $A_1D$, respectively $C_1D$.

a) Determine the measure of the angle of the planes $(AQP)$ and $(D_1RS)$.

b) Show that $\widehat{AQP} \equiv \widehat{D_1RS}$.