Geometry Problems, Online Education
Online Geometry Problem 874: Isosceles Triangle, Circumcircle, Circumcenter, Congruence. Level: High School, College, Mathematics Education

The figure below shows an isosceles triangle ABC (AB = BC) with a point D on AC. Prove that the circumcircles of triangles ABD and BDC are congruent.

 

Geometry problem 874: Isosceles Triangle, Circumcircle, Circumcenter, Congruence
 


 

Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given." 

Home | SearchGeometry | Problems | All Problems | Open Problems | Visual Index | 10 Problems | 871-880 | Triangles | Isosceles | Circle | Circumcircle | Angles | Email | Solution / comment | By Antonio Gutierrez