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In trapezium ABCD the side AB is parallel to the side DC, with AB = 12 and DC = 20. The diagonals AC and BD intersect at O. What is the ratio AO : OC?

Competition practiceGeometry
  • A5 : 3
  • B9 : 25
  • C2 : 3
  • D3 : 5

Step-by-Step Solution

Because AB ∥ DC, the alternate angles give triangle AOB similar to triangle COD. Corresponding sides are in the ratio AB : CD = 12 : 20 = 3 : 5, so AO : OC = 3 : 5.
Answer: D) 3 : 5

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