Question

AD‖BC,∠D=90,DC=7,AD=2,BC=3.若在边DC上有点P使△PAD与△PBC形似,则这样的P点有几个,请

Answer 1

设 PC = x, PD = 7 -x

则 △PAD与△PBC形似时

BC/PC = AD/PD

或

BC/PC = PD/AD

3/x = 2/(7-x)

或

3/x = (7-x)/2

从 3/x = 2/(7-x) 得到

2x = 21 - 3x

x = 21/5

从 3/x = (7-x)/2 得到

6 = x(7-x)

x^2 - 7x + 6 = 0

(x-1)(x-6) = 0

x = 1 或 x = 6

综上所述, 有3 个 P 点满足要求

PC = 1, 4.2, 和 6