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黑龙江省2002年中考数学试题第26题:已知等边△ABC和点P,设点P到△ABC三边AB、AC、BC的距离分别为h1、h2、h3,△ABC的高为h.“若点P在一边BC上(如图1),此时h3=0,可得结论:hl+h2+h3=h.”请直接应用上述信息解决下列问题:当点P在△ABC内(如图2)、点P在△ABC外(如图3)这两种情况时,上述结论是否还成立?若成立,请给予证明;若不成立,h1,h2、h3与h之间又有怎样的关系,请写出你的猜想,不需证明.A
The 26th problem of the 2002 Middle School Mathematics Exam Question in Heilongjiang Province: Knowing the equilateral △ABC and the point P, set the distance from the point P to the △ABC three sides AB, AC, and BC respectively as h1, h2, h3, and the height of △ABC is h “If the point P is on one side BC (as shown in Figure 1), and h3=0 at this time, you can get the conclusion: hl+h2+h3=h.” Please directly apply the above information to solve the following problems: When point P is within △ABC (Figure 2), point P outside the △ABC (Figure 3) these two cases, the above conclusion is still established? If it is, please give proof; if it is not established, there is another between h1, h2, h3 and h What kind of relationship, please write your conjecture without proof. A