Question

在三角形abc中角bac等于90度ab等于三ac等于四ad平分角bac交bc于d则bd的长为?

Answer 1

过D作DE⊥AC于E,
∵∠BAC=90°,∴DE∥AB,
∴∠BAD=∠ADE,
∵AD平分BAC,∴∠BAD=∠CAD,
∴∠DAC=∠ADE,
∴AE=DE,
∵CE/AC=DE/AB,
∴(4-DE)/4=DE/3,
4DE=12-3DE,
DE=12/7,
∴BD=12/7√2.