Question

在三角形ABC中,角ABC=2角C,BD平分角ABC,试说明:AB*BC=AC*CD

Answer 1

BD平分∠ABC
AB/BC=AD/CD
∠ABD=∠CBD=∠ABC/2
∠ABC=2∠C
∠ABD=∠C
∠A=∠A
三角形ABD∽三角形ACB
AB:AC=AD:AB
AD=AB^2/AC
AB/BC=AB^2/AC*1/CD
AB*AC*CD=AB^2*BC
AC*CD=AB*BC