GeoGebra is a free, open-source interactive learning and teaching tool designed for all  levels of education. It is a dynamic software that can be used for algebra, geometry, statistics, calculus, and graphical analysis.  GeoGebra is easy to learn and has an active international community of users, educators, and developers who support each other. It offers a rich set of tools and enables users to input geometric objects (points, lines, vectors, ellipses, etc.) and algebraic expressions (variables, functions, derivatives, integrals, etc.). Most importantly, it enables the students to manipulate these objects and expressions dynamically. GeoGebra can be downloaded and installed onto your computers and mobile devices or it can used used online.

Here is the geometry problem (Source: Dr. Andrew Adler, UBC) that I posed in our 2015/01/13 SyMETRI meeting:

Triangle ABC is right-angled at C. The bisector of <ACB meets AB at L. If BC = a
and AC = b, find the distance between the orthocenters of  triangles ALC and BLC.

Hint: The distance between the orthocenters (O and P) involves a relationship between the sum and difference of the legs, and the hypotenuse of the triangle.