Proof: Because AB=AC, ∠ B = ∠ C.
When exercise time is 1S, BP=CQ=3.
D is the midpoint of AB, so BD=AB/2=5.
CP=BC-BP=8-3-5
BD=CP
At △BPD and △CQP
BP=CQ,∠B=∠C,BD=CP
So △ BPD △ CQP (SAS)
② If the speeds of P and Q are not equal, then BP≠CQ.
Therefore, if two triangles are congruent, BP=CP, BD=CQ=5.
BP=CP=BC/2=4
Therefore, the movement time is 4/3 seconds.
Q Motion speed: 5÷4/3= 15/4.
(2) Since both points rotate counterclockwise, P leads Q20 cm(Q when starting (Q will catch up with P).
Let the distance traveled by P at the first meeting be X cm, and the distance traveled by Q be X+20 cm.
X/3=(X+20)/( 15/4)
Cross multiplication: 15X/4=3X+24
3X/4=60
X=80
So it takes 80/3 seconds to meet.
80-2( 10+ 10+8)=24
18 < 24 < 28, so we met at AB.