latura AB a triunghiului isoscel ABC([AB]=[BC])este si diametrul cercului care intersecteaza latura BC in punctul D,astfel incat BD/DC=4 si AC=sqrt5.Calculati aria triunghiului ABC.

BD/DC=4=> BD=(4/5)DC si DC=(1/5)BC
AB diametru =>ABD si ADC triunghi dr.
AB^2=AD^2+BD^2
AB=BC =>BC^2=AD^2+BD^2 =>BC^2=AD^2+(16/25)BC^2 =>(9/25)BC^2=AD^2=>AD=(3/5)BC
aria =(BC*AD)/2=[BC*(3/5)BC]/2=(3/10)BC^2
AD^2+DC^2=AC^2 =>(9/25)BC^2+(1/25)BC^2=AC^2 =>(10/25)BC^2=5=>
=>BC^2=25/2
ARIA = (3/10)*(25/2)=15/4

[Citat] BD/DC=4=> BD=(4/5)DC si DC=(1/5)BC AB diametru =>ABD si ADC triunghi dr. AB^2=AD^2+BD^2 AB=BC =>BC^2=AD^2+BD^2 =>BC^2=AD^2+(16/25)BC^2 =>(9/25)BC^2=AD^2=>AD=(3/5)BC aria =(BC*AD)/2=[BC*(3/5)BC]/2=(3/10)BC^2 AD^2+DC^2=AC^2 =>(9/25)BC^2+(1/25)BC^2=AC^2 =>(10/25)BC^2=5=> =>BC^2=25/2 ARIA = (3/10)*(25/2)=15/4

nu am inteles dc 4/5 si 1/5

BD/DC=4 =>BD=4DC
BD+DC=BC =>4DC+DC=BC =>5DC=BC =>DC=(1/5)BC
BD=BC-DC=BC-(1/5)BC=(4/5)BC