如图,若PA=PB,∠APB=2∠ACB,AC与PB交于点D,且PB=4,PD=3,则AD•DC=_.

问题描述:

如图,若PA=PB,∠APB=2∠ACB,AC与PB交于点D,且PB=4,PD=3,则AD•DC=______.

以P为圆心,以PA=PB为半径作圆,延长BD交圆于M,如图:PA=PB=4,∠APB=2∠ACB,AC与PB交于点D,PD=3,
设∠ACB=θ,则∠APB=2θ,又∠ACB=θ,∴C在圆上.
∴AD•DC=BD•DM=BD•(PM+PD)=1•(4+3)=7,
故答案为 7.