les digonales d′un quadrile^� re ABCD (inscriptible) se coupent en O on note AB=a ; BC=b ; CD=c ; AD=d ; OA=e OB=f ; Oc=g ; OD=h montrer que: (a/c)+(c/a)+(b/d)+(d/b)≤(e/g)+(g/e)+(f/h)+(h/f)


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Question Number 160649 by Eric002 last updated on 04/Dec/21

$l e s d i g o n a l e s d^{'} u n q u a d r i l \overset{`}{e r e} A B C D$ $(i n s c r i p t i b l e) s e c o u p e n t e n O o n n o t e$ $A B = a; B C = b; C D = c; A D = d; O A = e$ $O B = f; O c = g; O D = h$ $m o n t r e r q u e :$ $\frac{a}{c} + \frac{c}{a} + \frac{b}{d} + \frac{d}{b} ⩽ \frac{e}{g} + \frac{g}{e} + \frac{f}{h} + \frac{h}{f}$
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