MathDB

Let

ABCDEF

be a regular hexagon with side length

a

. At point

A

, the perpendicular

AS

, with length

2a\sqrt{3}

, is erected on the hexagon's plane. The points

M, N, P, Q,

and

R

are the projections of point

A

on the lines

SB, SC, SD, SE,

and

SF

, respectively. [*]Prove that the points

M, N, P, Q, R

lie on the same plane. [*]Find the measure of the angle between the planes

(MNP)

and

(ABC)

Problem Statement