Currently, many researches investigate teaching practice in search of teaching and learning with good results, however, there are still many difficulties encountered. In this context, the present work has as general objective to investigate the contributions of the methodological use of research activities of geometry through digital books for mathematical learning. For this, it presents as specific objectives: to elaborate and to apply a sequence of activities on the relations that exist between the angles in the circumference; identify whether students can recognize and write patterns; to analyse the students' development regarding the formalization of ideas from standards; Identify whether students feel motivated to participate in activities. We present a methodological proposal on how to explore geometry in an investigative way, focusing on the relationships between the angles in a circle. It is a qualitative research based on the observation and interaction of the author with the students during the application of the activities and in the production of their investigations, besides an opinion questionnaire. The application of the activities was consolidated with high school students of the Campus Caicó - IFRN. In the results, the methodology was observed as a facilitating and motivating aspect of learning, emphasizing the importance of the use of differentiated methodological strategies