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This essential trains for: SAT-I, SAT-II, GMAT, AMC-8.

To solve solid geometry problems we try to reduce them to plane geometry problems.

There are two main ways of turning a 3D figure into a 2D one:

Projecting a 3D figure To project onto a plane means to drop perpendiculars from points of the solid onto the plane and connect them appropriately.

figure

Sectioning a 3D figure To section means to cut. The shape of the cut is called 'the section'.

figure

By cutting (sectioning) a cone or a pyramid with a plane parallel to the base, we obtain a truncated cone or pyramid.

figure

where, from the plane section VOAB:

equation

(Interior or Exterior) Tangent spheres have the same property as tangent circles: the segment that connects the two centers passes through the point of contact.

figure