Here is a problem that I thought up (probably has appeared somewhere before but I have not seen it) which is presented in the GeoGebra applet below.  We are early in the school year (well, except for some southern hemisphere schools) and I like to set the tone from the start of any mathematics course I teach that confident application of problem solving skills is a key ingredient of enjoying mathematics - and being successful on written exams - in both SL maths and HL maths.

For many more problems (currently 377) I've composed ("problems", not "exercises") see my growing lists of problems (one for SL and one for HL) at Problem of the Day.

The answer (and solution) to the problem is posted here.  Any feedback is warmly welcomed.  Enjoy.