In rectangular trapezoid ABCD. Ad = 7 & nbsp; & nbsp; ab = 2 & nbsp; & nbsp; DC = 3 & nbsp; & nbsp; P is a point on ad. the triangle with the vertex of P, a and B is similar to the triangle with the vertex of P, D and C. how many such points P have? Why?

In rectangular trapezoid ABCD. Ad = 7 & nbsp; & nbsp; ab = 2 & nbsp; & nbsp; DC = 3 & nbsp; & nbsp; P is a point on ad. the triangle with the vertex of P, a and B is similar to the triangle with the vertex of P, D and C. how many such points P have? Why?

There are three such p-points for the following reasons: ∵ a = ∠ d = 90 ° there are two situations in this question: ① if ABCD = apdp, then 23 = AP7 − AP, ∵ AP = 145; ② if ABPD = APCD, then 27 − AP = AP3, ∵ AP = 1 or 6, that is, there are three p-points

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