Difficult geometry problem

bator

New member
Joined
Nov 15, 2021
Messages
1
IMG_20211115_174852.jpg
ABCD is a square with a side length of 1. A set of parallel lines with distance 1 between them overlap the square. P, Q, R and S are the points of intersection resulted from the overlapping.
Find theta.

I've realized that the opposite figures inside the square are similar, and have tried substituting different lengths with x and y but nothing seems to work.

Help would be appreciated, thanks!
 
Have you posted the whole question? I think the value of θ depends on the angle between the lines AB and PQ.
 
Have you posted the whole question? I think the value of θ depends on the angle between the lines AB and PQ.
Sketching in CAD produced the same 45 degree θ for multiple angles between AB and PQ.
 
Hint: in the attached drawing consider triangles BDF and ACG
 

Attachments

  • d2.pdf
    19.3 KB · Views: 5
View attachment 29724
ABCD is a square with a side length of 1. A set of parallel lines with distance 1 between them overlap the square. P, Q, R and S are the points of intersection resulted from the overlapping.
Find theta.

I've realized that the opposite figures inside the square are similar, and have tried substituting different lengths with x and y but nothing seems to work.

Help would be appreciated, thanks!
Any progress?
 
Top