2004年高考湖北卷第19题是这样的:如图1,在Rt△ABC中,已知BC=a,若长为2a的线段PQ以点A为中点,问PQ与BC的夹角θ取何值时BP.CQ的值最大?并求出这个最大值.(解略)下面我们考虑更一般的情况:图1图2如图2所示,已知△ABC中,|BC|=a,|CA|=b,|AB|=c,PQ是以A为圆心,r为半径的圆的直径,求 In the 2004 college entrance examination Hubei paper, the 19th question is this: As shown in Figure 1, in RtΔABC, BC=a is known. If the line PQ of length 2a has point A as the midpoint, ask the angle between PQ and BC. Which value is the maximum value of BP.CQ? And find this maximum value. (Solution omitted) Let’s consider the more general situation: Figure 1 Figure 2 As shown in Figure 2, known △ ABC, |BC|= a,|CA|=b,|AB|=c, PQ is the diameter of a circle with A as the center and r as the radius.