(March (2) 2004. problem 3) Given line p(P,K(K', OK₀)) and point A (A', OA₀) that does not belong to p. Construct orthogonal projection of the  pyramid  ABCDV with height  SV belonging to p, and  edge AV that makes angle 60^o with the projection plane  p.

Resenje:

Layer 01: We draw given elements..

Layer 02: Let m = AV be edge of the pyramid. It belongs to the plane g = (A,p) = (AK, p). We can construct the trace  L of line  l = AK since it also belongs to the trace of the plane g.

Layer 03: Since p Ì g, we have P Î c, where c is trace of  g, and hence c = PL.

Layer 04: Edge m belongs to the g, so its trace M belongs to c. Since m ' A i Ð(m, p) = 60^o, trace M belongs to the circle k with center A'  that one can construct using well known procedure. Hence, one can construct point M as an intersection cÇk. One also finds  m' = MA'. The projection  V' is intersection m'×p'.

Layeri 05 i 06: The base plane t of the pyramid, contains A and is orthogonal to the line  p and hence t is determined. Denote its trace by t. We also construct the intersection S = p×t which is the center of the base.

Layer 07: Using common procedure we rotate plane  t (and also point A) around its trace.

Layeri 08 i 09: Using the rotated images of  A i S we can determine the rotated points of the base. Then, by rotating the base back we get  the projection A'B'C'D' of the base..

Layer 10: Projection of the base.

---

File translated from T_EX by T_TH, version 3.56.
On 11 May 2004, 18:29.