Thales, circumcircle and tangent
Prove the Satz des Thales and its converse, find the circumcircle of a triangle, and construct a tangent with the Thaleskreis.
- France: grade 7
- Germany: grade 7
- Syria: grade 7
- Palestine: grade 9
- Ukraine: grade 7
Guide
The Satz des Thales says: if C lies on the circle with diameter AB, then the angle at C is 90°. Its converse also holds, so the circle contains exactly the points with a right angle.
The perpendicular bisectors of the three sides meet in the centre M of the Umkreis. The angle bisectors meet in the centre of the Inkreis.
A tangent is perpendicular to the radius at the point of contact. With the Thaleskreis you can construct the tangents from a point outside the circle. Proofs are written as Voraussetzung, Behauptung, Beweis.