Gogeometry Problem 268

 dans Euclide Geometry Problem par Harvey Littleman

---

From Gogeometry

Using :

• Pythagoras
• Area of a triangle

Define c=AB

S=[ABC]=a.b/2=c.h/2 => a.b=c.h

c=a.b/h => c^2=a^2.b^2/h^2

Pythagoras => a^2+b^2=c^2

=> a^2+b^2=a^2.b^2/h^2

dividing by a^2.b^2 => 1/b^2 + 1/a^2 = 1/h^2

 

---

---