BP=8-2=6

BQ=2*2=4

PQ=√6？ +4? =2√ 13

② When t≤3

BP = 8t，BQ=2t

8-t=2t, and t=8/3 is obtained.

When t > 3

AP=t，BP=8-t，CQ=2t-6，AQ= 16-2t

PQ？ =( 16-2t)？ +t？ -2t( 16-2t)*4/5

=8.2t？ -64t+230.4

BQ？ =36+(2t-6)？ -2*6*(2t-6)*3/5

=4t？ -38.4t+ 1 15.2

When PQ=BQ, 8.2t? -64t+230.4=4t？ -38.4t+ 1 15.2, the equation has no solution.

When BP=PQ, 8.2t? -64t+230.4=(8-t)？ This equation has no solution.

When BP=BQ, 4t? -38.4t+ 1 15.2=(8-t)？ This equation has no solution.

To sum up, when t=8/3, △PQB is an isosceles triangle.

③AP=t，BP=8-t，CQ=2t-6，AQ= 16-2t

BQ？ =36+(2t-6)？ -2*6*(2t-6)*3/5

=4t？ -38.4t+ 1 15.2

When BC=CQ, that is, 2t-6=6, t=6 is obtained.

When BQ=BC, that is, 4t? When -38.4t+ 1 15.2=6, the equation has no solution.

When BQ=CQ, that is, 4t? -38.4t+ 1 15.2=(2t-6)？ ，t=5.5

To sum up, when t=5.5 or t=6, △BCQ is an isosceles triangle.