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." 

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