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Online Geometry Problem 740: Scalene Triangle, Angle, Semi-sum, Cevian, Isosceles Triangle. Level: High School, Honors Geometry, College, Mathematics Education

The figure shows a triangle ABC so that D is on AC and the angle ADB is the semi-sum of angles ABC and ACB. Prove that AB = AD (isosceles triangle).
 

 Geometry problem, isosceles triangle, angle, exterior angle
 

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