Thursday, August 18, 2011

Problem 658: Triangle, Altitudes, Diameter, Circle, Angles

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

Click the figure below to see the complete problem 658.

 Online Geometry Problem 658: Triangle, Altitudes, Diameter, Circle, Angles.

2 comments:

  1. AF^2 = AD.AC
    AG^2 = AE.AB
    But AD.AC = AE.AB since B,E,D,C are concyclic
    Follows AF = AG, angles AFG = AGF = x
    Now CF^2 = CD.CA = CG.CH
    Follows angles CFG = CHF = y say
    Hence x + y = AFG + CFG = AFC = 90 deg
    Therefore x = 90 - y = 90 - 12 = 78 deg

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  2. Why do you state that CD.CA = CG.CH ?

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