Skip over navigation
Where does the plane $PDQ$ meet the line $EH$?
Imagine a vertical line through $A$. Where does the plane $PDQ$ meet this line?
The method only needs similar triangles and similar 3D shapes.
It is not necessary, but it may help, to use coordinates with the origin at $A$.
Plane to See
Age 16 to 18
Challenge Level 
Where does the plane $PDQ$ meet the line $EH$?
Imagine a vertical line through $A$. Where does the plane $PDQ$ meet this line?
The method only needs similar triangles and similar 3D shapes.
It is not necessary, but it may help, to use coordinates with the origin at $A$.
You may also like
Wrapping Gifts
A box of size a cm by b cm by c cm is to be wrapped with a square piece of wrapping paper. Without cutting the paper what is the smallest square this can be?
Four Points on a Cube
What is the surface area of the tetrahedron with one vertex at O the vertex of a unit cube and the other vertices at the centres of the faces of the cube not containing O?
Instant Insanity
We have a set of four very innocent-looking cubes - each face coloured red, blue, green or white - and they have to be arranged in a row so that all of the four colours appear on each of the four long sides of the resulting cuboid.