AB^2=AC^2+BC^2= 100？ AB= 10

CD=AB/2= 10/2=5

1，AB*CE=AC*BC CE=AC*BC/AB=4.8

2.BQ=2t？ CP=t？ PD=CD-CP=5-t

PD:CD=PF:CE？ PF = PD * CE/CD =(5-t)* 4.8/5 = 4.8-0.96t

S(PQB)=BQ*PF/2=4.8t-0.96t^2

y=4.8t-0.96t^2

When t=-b/2a=2.5, y has a maximum value: y=6.

3.？ When PQD is an isosceles triangle

QD=BD-BQ=5-2t？ (Qpoint is on BD) QD=QP, QP=PD is invalid.

QD=BQ-BD=2t-5 (Q point is on AD)

de^2=cd^2-ce^2= 1.4 df:de = PD:CD df = 0.28(5-t)

QF = QD-DF = 2t-5-0.28(5-t)= 2.28t-6.9？ PQ^2=QF^2+PF^2

a，QD=DP，

When QD=BQ-BD=2t-5, 2t-5 = 5t? t= 10/3

When QD=BQ-BD=5-2t, 5-2t=5-t? t=0？

b、QD=PQ sin(CDE)=CE/CD=0.96？ QD=PQ ∠QDP=∠QPD=∠CDE

PQ =(PD/2)/sin(CDE)=(5-t)/ 1.92

PQ=QD

(5-t)/ 1.92=2t-5

4.84t= 14.6

t=365/ 12 1

c，DP=PQ？ ∠QDP=∠PQD=∠CDE？ cos(CDE)=DE/CD=0.28

PQ=(QD/2)/sin(CDE)=(2t-5)/0.28

5-t=(2t-5)/0.28

2.28 tons =6.4

t= 160/57？