Current location - Training Enrollment Network - Mathematics courses - The problem of straight line in mathematics competition
The problem of straight line in mathematics competition
Mathematical competition questions are difficult to answer, and partial derivatives should be used normally.

The distances from the three vertices A, B and C of a right triangle surrounded by three straight lines to AB, BC and AC are D 1, D2 and D3, respectively, as follows:

| AB | * d 1+| BC | * D2+| AC | * D3 = 2S(ABC)

And (| AB | * D 1+| BC | * D2+AC * D3) 2.

So d12+d22+d32 > = 4s (ABC)/(| AB | 2+| BC | 2+| AC | 2) =128/5.

The equal sign is true if and only if |AB|/d 1=|BC|/d2=|AC|/d3.

You should be able to handle it yourself, right? Hehe, I wonder if it will help.