Geometry Problem 1305

Triangle, Circumcircle, Angle Bisector, Arc, Perpendicular, Area

The figure below shows a triangle ABC with the circumcircle of center O. The bisector of the angle A cuts BC at D and the arc BC at E. If DH is perpendicular to AC, prove that the area of the triangle AEH is half the area of the triangle ABC. See also: Art of Problem 1305, Typography using iPad Apps.


Geometry Problem 1305 Triangle, Circumcircle, Angle Bisector, Arc, Perpendicular, Area
 

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Triangle
Circle
Circumcircle
Angle Bisector
Perpendicular lines
Triangle Area


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Problem 1305 in Motion using Mobile Apps, iPad

Click on the figure below.

 

 

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