Because AD is perpendicular to EF, and? If AEF is a right triangle, then there is an angle AFE= = angular bud, and angular DAC= = angular AEF.

In ABD, sinbad/sinb = BD/ad —————1.

In ACD, sincad/sinc = DC/ad ————————— 2.

And then what? In ABC, angle B = angle c, so if 1 is divided by 2, there is sinBAD/sinCAD=BD/CD.

That is AE/af = BD/CD.