问题补充:
半径为4的球面上有A,B,C,D四点,且满足AB⊥AC,AC⊥AD,AD⊥AB,则S△ABC+S△ACD+S△ADB的最大值为(S为三角形的面积)________.
答案:
32
解析分析:设AB=a,AC=b,AD=c,根据AB⊥AC,AC⊥AD,AD⊥AB,可得a2+b2+c2=4R2=64,而S△ABC+S△ACD+S△ADB=(ab+ac+bc),利用基本不等式,即可求得最大值为.
解答:设AB=a,AC=b,AD=c,∵AB⊥AC,AC⊥AD,AD⊥AB,∴a2+b2+c2=4R2=64∴S△ABC+S△ACD+S△ADB=(ab+ac+bc)≤(a2+b2+c2)=32∴S△ABC+S△ACD+S△ADB的最大值为32故
半径为4的球面上有A B C D四点 且满足AB⊥AC AC⊥AD AD⊥AB 则S△ABC+S△ACD+S△ADB的最大值为(S为三角形的面积)________.