Question

已知△ABC中,AB=AC,∠B=36°,点D在BC上,且AD=DC,则AD:AC=

Answer 1

设AB=AC=1,AD=CD=x,∵∠B=36°,∴∠C=36°,∴∠BAC=108°,又DA=DC,∴∠DAC=36°,∴∠BAD=72°,∴∠BDA=72°,∴BD=BA=1,∴BC=1＋x,∴△ABC∽△DAC,∴AB∶DA=BC∶AC,∴1∶x=﹙1＋x﹚∶1,∴x²＋x－1=0,解得：x=...