Question

已知∠A为定角,P、Q分别在∠A的两边上,PQ为定长,当P、Q处于什么位置时,△APQ的面积最大?

Answer 1

S△ABC=1/2*AP*AQsinA

cosA

=(AP^2+AQ^2-PQ^2)/(2AP*AQ)

≥（2AP*AQ-PQ^2)/(2AP*AQ),此时AP=AQ

=1-PQ^2/(2AP*AQ)

cosA≥1-PQ^2/(2AP*AQ)=1-PQ^2sinA/(4S)

S≤PQ^2sinA/(4-4cosA)

AP=AQ时

Smax=PQ^2sinA/(4-4cosA)