如图:在△ABC中,BC=5,延长BC至点D,使∠DAC=∠B,AD=6,则CD=_.

问题描述:

如图:在△ABC中,BC=5,延长BC至点D,使∠DAC=∠B,AD=6,则CD=______.

∵∠DAC=∠B,∠D=∠D,
∴△ABD∽△CAD,

AD
CD
=
BD
AD

∵BC=5,AD=6,
∴(5+CD)CD=36,
即得CD=4.
故答案为:4.