olymmath

HMMT 2009 K7

  • Calculus
  • Answer

A line in the plane is called strange if it passes through (a,0)(a, 0) and (0,10−a)(0,10-a) for some aa in the interval [0,10][0,10]. A point in the plane is called charming if it lies in the first quadrant and also lies below some strange line. What is the area of the set of all charming points?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{50}{3}

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