AB=√(AC？ +BC？ )=√(6? +8? )= 10

AD=AB/2=5

AP=2t

AQ=AD+ 1t=5+t

The first question:

When AP/AC=AQ/AB, PQ and BC are connected in parallel.

2t/6=(5+t)/ 10

(2/3- 1/5)t= 1

7/ 15t= 1

t= 15/7

When t= 15/7, PQ is parallel to BC.

The second question:

Sina =BC/AB=8/ 10=4/5.

Y = S△APQ = 1/2AP * AQ * Sina = 1/2*2t(5+t)*4/5 = 4/5t? +4t

The third question:

s△ABC = 1/2BC * AC = 1/2 * 8 * 6 = 24

S△APQ = 7/ 15S△ABC

4/5t？ +4t = 7/ 15*24 = 56/5

t？ +5t - 14 = 0

(t+7)(t-2)=0

t+7≥7

∴t-2=0

t=2

When t=2, the ratio of △APQ to △ABC area is 7: 15.