Have a look at the excellent resource collection on the Nrich GeoGebra page. Look at the area of a parallelogram or perhaps explore Addition of Complex Numbers with Further Mathematics Students. Using applets such as these can help students pose questions to investigate and lead to greater insights into the problem.
Searching for the same title on Nrich returns the problem. Searching on Nrich Isosceles Triangles, for example, takes us to a problem where we need to find isosceles triangles with a given vertex which have an area of 9. As always on Nrich we can look at Teachers’ resources and a solution. Looking at the Teacher’s Resources for Isosceles Triangles, for example, we see a commentary from Paul Andrews on why he likes the problem. This problem is included in the lovely Nrich poster collection. Nrich has really useful links to related resources, here we have a proof question for age 11-14 or a collection of resources where students must find all solutions.
Alternatively, search Nrich for problems which can be explored with GeoGebra.
Another collection of resources which can be explored with GeoGebra comes from MEI. For applets available to use, check the GCSE resources available here.
If you want to learn more about GeoGebra and also look at some great tasks for thinking and understanding then these GCSE and A Level tasks provide clear instructions for constructing objects in GeoGebra and pose questions to help students explore many areas of Mathematics. MEI has designed the tasks so they can be accessed using the computer-based version of GeoGebra or the tablet/smartphone app. Each task instruction sheet is reproducible on a single piece of paper and they are designed to be an activity for a single lesson or a single homework task (approximately).
As MEI state:
These tasks are designed to help students in understanding mathematical relationships better through exploring dynamic constructions.
These tasks for Further Pure Mathematics provide an excellent way for exploring several topics in the Pure content for Further Mathematics.
My file with the subject of content for Maths and Further Maths with links to resources using technology has been updated with the resources in this post. This can be found on my Use of Technology page.
These resources have been added to the GeoGebra Series of pages.