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In trapezium ABCD, AB is parallel to DC and the diagonals meet at O. If AB = 8 cm and DC = 14 cm, find AO : OC.

Class 10Basic Proportionality TheoremGeometry — Similarity
  • A7 : 4
  • B4 : 7
  • C4 : 11
  • D16 : 49

Step-by-Step Solution

Triangles AOB and COD have equal vertically opposite angles at O and equal alternate angles (AB parallel to DC), so AOB is similar to COD. Hence AO : OC = AB : DC = 8 : 14 = 4 : 7. Picking 7 : 4 turns the ratio upside down; 4 : 11 gives AO : AC (part to whole) instead of AO : OC (part to part); 16 : 49 is the ratio of the areas of the two triangles, not of the segments.
Answer: B) 4 : 7

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