British Flag Theorem
Geometry
Level
pending
In rectangle ABCD, AB=5 and CD=13. Let us choose a random point P inside of rectangle ABCD. What is the expected value of
The answer is 0.
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1 solution
The British Flag Theorem tells us that for any point P inside of rectangle ABCD, ( A P ) 2 + ( C P ) 2 = ( B P ) 2 + ( D P ) 2 thus for any point P inside the rectangle ( A P ) 2 + ( C P ) 2 − ( B P ) 2 − ( D P ) 2 = 0 thus our answer is 0