(untitled) (mathematica didactica, 2021)
Theorems about inscribed angles in circles and intersecting chords allow a deeper understanding of various geometric constellations from right angled triangles to kinematically generated curves. The similarity theorems in a circle are not immediately apparent from the consideration of the respective configuration. However, by experimentation they reveal deeper structure and beauty. We show how this content allows and inspires learning by discovery in teacher education. Our examples are related to canonical themes in the study of mathematics education, such as concept development, problem solving and the educational aspects of proving. In addition to these topics, we use the example to give an introduction into the development