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The diagonals of quadrilateral ABCD meet at O. Which statement is true?

Class 7Triangle InequalityTriangles
  • AAB + BC + CD + DA = AC + BD
  • BAB + BC + CD + DA > 2(AC + BD)
  • CAB + BC + CD + DA < AC + BD
  • DAB + BC + CD + DA < 2(AC + BD)

Step-by-Step Solution

Triangle OAB: AB < OA + OB; similarly BC < OB + OC, CD < OC + OD, DA < OD + OA. Adding: perimeter < 2(OA + OB + OC + OD) = 2(AC + BD).
Answer: D) AB + BC + CD + DA < 2(AC + BD)

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