Friday, September 9, 2011

Problem 666: Intersecting Circles, Secant, Tangent, Concyclic points, Mind Map

Geometry Problem
Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the complete problem 666.

 Problem 665: Intersecting Circles, Secant, Tangent, Angles, Mind Map.


  1. angle CBD + angle CED
    = (angle CBA + angle ABC)+ angle CED
    = angle ECD + angle EDC + angle CED (*)
    = 180 degrees
    => E, C, B, D are concyclic

    (*)angle between chord and tangent = angle in the
    alternate segment

  2. from previous problem, <ABE= <CDE-<ECD, and it is known that <ABD=<CDE, thus <EBD=<ECD and we are done.