Geometry and a Square - A game with right angles.
Air Strike - Find a maximum set of points covered by two disks.
Build the Fence - Convex hull, huh?
Cell Phone - Cover maximum points with one disk.
Transmitters - Sort points along the rotation angle.
The Ant - Find a route for a little ant.
Equipment Box - Does one rectangle fit into another?
Lifting the Stone - A search for the center of mass.
Almost Shortest Path - Find an almost shortest path.
Lego - Did you use to play Lego? Then this shouldn't be a challenge for you!
Ant - Ants know nothing about matrix multiplication and fast exponentiation.
Paradox - Identify a contradiction in a set of arguments.
The Bottom of a Graph - Find a bottom of a graph.
http://www.spoj.com/problems/GEOPROB/
http://www.spoj.com/problems/JASIEK/
http://www.spoj.com/problems/CVXPOLY/
http://www.spoj.com/problems/VCIRCLES/
http://www.spoj.com/problems/AE5B1/
http://www.spoj.com/problems/RUNAWAY/
http://www.spoj.com/problems/CONDUIT/
http://www.spoj.com/problems/TETRA/
http://www.spoj.com/problems/QUADAREA/
http://www.spoj.com/problems/TRICENTR/
http://uva.onlinejudge.org/external/117/11796.html
You may also want to explore more basic and advanced geometric concepts using
free online tool:
http://www.geogebra.org/webstart/geogebra.html