An important and interesting area in the study of triangle geometry is the related issue of extrema problems and inequalities. These problems play a significant role in the mathematics study program in high school. In tasks such as these, the difficulty level is high when one does not know in advance what the expected answer is. When one knows what to prove, the difficulty level is lower and most of the effort is aimed at attaining a proof of the expected answer. This can be done using dynamic geometric software. The possibility of making frequent changes to the geometric objects and the ability of dragging objects, contributes to the process of deducing properties, checking hypotheses and generalizing. In this paper, eight investigative tasks in Euclidean geometry are presented together with the applets developed for carrying out the dynamic investigation. Some of the tasks are well known, while others are almost unknown and are worthy of presentation as enrichment for those interested in the subject. The tasks were given to preservice teachers of mathematics as part of an advanced course for integrating technological tools in the teaching of mathematics.