fie AM -proiectia lui AOpe AB
MB=AB-AM=13-9=4cm
in ΔAOB-dreptunghic;
[tex]MO^2=AM*MB;MO= \sqrt{9*4}=6cm [/tex]
dinΔAMO-dreptunghic
[tex]AO= \sqrt{AM^2+MO^2} = \sqrt{81+36}= \sqrt{117}=3 \sqrt{13 }cm \\ AC=2AO=6 \sqrt{13}cm [/tex]
[tex]AC^2+BD^2=4AB^2 \\ 36*13+BD^2=4*169;BD= \sqrt{4*169-36*13}= \sqrt{676-468}= \\ = \sqrt{208}=[tex]4 \sqrt{13}cm [/tex]
[tex]A =\frac{AC*BD}{2} = \frac{6 \sqrt{13}*4 \sqrt{13} }{2}=156cm^2 [/tex]
