Дано: АВСВ - паралелограм, Р=48 см., СМ - бісектриса, DM : MA = 5 : 2. Знайти АВ=СD, AD=BC.
∠BCM=∠MCD за умовою
∠CMD=∠МСВ як внутрішні різносторонні при АD║ВС та січній СМ, отже
∠CMD=∠MCD, ΔMCD - рівнобедрений, СD=MD.
Нехай АМ=2х см, МD=5х см, СD=5х см, ВС=2х+5х=7х см, АВ=5х см.
2(5х+7х)=48
12х=24; х=2.
АВ=СD=5*2=10 см, AD=BC=7*2=14 см.
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