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Segment DE joins a point D on AB to a point E on AC of triangle ABC and is parallel to BC. If AB = 21 cm and DB = 12 cm, find AE : EC.

Class 10Basic Proportionality TheoremGeometry — Similarity
  • A4 : 3
  • B3 : 7
  • C3 : 4
  • D12 : 21

Step-by-Step Solution

First recover the missing part: AD = AB − DB = 21 − 12 = 9 cm. By BPT, AE : EC = AD : DB = 9 : 12 = 3 : 4. Choosing 4 : 3 reverses the order of the two segments; 3 : 7 is AD : AB, the part-to-whole ratio, which is the commonest BPT mix-up; 12 : 21 is DB : AB, again part to whole and with the parts swapped.
Answer: C) 3 : 4

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