Problem 976

 dans Euclide Geometry Problem  étiqueté 45 Degrees / Angle Bisector / Hypotenuse / Incenter / Isosceles Right Triangle par Harvey Littleman

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From Gogeometry

Using :

• Pythagoras
• Inradius in right triangle

• Define r as the inradius of ΔABC
• in a right triangle, r=(AB+BC-AC)/2
• AB=AC => r=(2AB-AC)/2=AB-AC/2
• BI=r.sqrt(2)=sqrt(2)(AB-AC/2)=sqrt(2).AB-AC/sqrt(2)
• AC=sqrt(2).AB => BI=AC-AB
• Therefore AC=AB+BI

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