Question

.在三角形ABC中,∠B.∠C的平分线交于点O,OD垂直BC于O,如果AB=15cm,BC=25cm,AC=20cm,`

Answer 1

∵AB=15cm,BC=25cm,AC=20cm

∴AB^2+AC^2=BC^2

∴∠A=90°

做OE⊥AB于E,OF⊥AC于F

∵BO是∠B的角平分线,∴OD=OE

∵CO是∠C的角平分线,∴OD=OF

又：OE⊥AB,OF⊥AC

∴AEOF为正方形

令AE=AF=x

则EB=AB-x=15-x,FC=AC-x=20-x

又：BE=BD,CF=CD,BD+CD=BC

∴15-x+20-x = 25

-2x = -10

x = 5

即OD=5