As can be seen from the figure, CM=PD=2t and CQ = t. If the triangle with B, P and Q as its vertices is an isosceles triangle, it can be divided into three situations:

(1) if PQ=BQ, in Rt△PMQ, pq 2 = t 2+ 12 2, which is obtained from t 2+ 12 2 = (16-t) 2 of pq 2.

t = 7/2；

② if BP=BQ, in Rt△PMB, Pb 2 = (16-2t) 2+ 12 2, which is obtained from Pb 2 = bq 2, (16-2t) 2+ 12.

③ If PB=PQ, it is derived from Pb 2 = PQ 2 and t 2+12 2 = (16-2t) 2+12 2.

T 1= 16/3，t2= 16。

All in all, when

T = 7/2 seconds or

When t= 16/3s, the triangle with B, P and Q as vertices is an isosceles triangle.