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,请列举
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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