Kẻ DH⊥AB,CM//AD
⇒AH=ADcos60o=12|→b|
Do hình
thang ABCD cân ⇒AM=CD=AB−2AH=|→a|−|→b|
⇒BM=AB−AM=|→b|
→BC=→BM+→MC=−→|b|→|a|→a+→b
→AC=→AD+→AM=→b+→a−→|b|→|a|→a
→BD=→BA+→AD=→b−→a
→AC⊥→BD⇔→AC.→BD=0⇔(→b+→a−→|b|→|a|→a)(→b−→a)=0
⇔2a2−2ab−b2=0(do →a.→b=a.b.cos60o)
⇒a=b2(1+√3)