ABCD is a quadrilateral whose diagonals AC and BD intersect at O. If triangles AOB and COD have areas 4 and 9 respectively, then the minimum area that ABCD can have is
Question and options
ABCD is a quadrilateral whose diagonals AC and BD intersect at O. If triangles AOB and COD have areas 4 and 9 respectively, then the minimum area that ABCD can have is
- 26
- 25
- 21
- 16
Answer and explanation
Correct answer: B - 25
Area(AOB)*Area(COD) = Area(BOC)*Area(AOD) = 36 (areas are proportional to diagonal segments). By AM-GM, BOC+AOD >= 2*sqrt(36) = 12, so minimum total = 4+9+12 = 25.
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IPMAT Indore
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