Angle B= angle c

Angle BPA= Angle PAC+ Angle C= Angle PAC+ Angle APM= Angle PMC.

Obtain triangle similarity

2

Classification discussion, let PB=X,

When AP=PM, 8-X=5, X=3.

AP=AM, which is invalid.

When AM=PM=Y, AP=PC=8-X, 5: 8-x = x: 5-y = 8-x: y.

5Y=X - 16X+64

25-5Y=8X-X squared

25 X squared+16X-64=8X-X squared

8X=39

X=39/8