In trapezium ABCD, AD∥BC, O is intersection point of diagonals BD and AC. Points F and E are on AB and CD, respectively such that FE passes through point O. If BC = 5 cm and AD = 20 cm, then, the length of EF is – 

  1. 8 cm
  2. 12 cm
  3. 10 cm
  4. 15 cm

Answer (Detailed Solution Below)

Option 1 : 8 cm
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Detailed Solution

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Given:

AD/BC

BC = 5 cm and AD = 20 cm

Concept used:

If AD = a and BC = b

⇒ EF = (2a.b)/(a + b)

Calculation:

F8 Aashish S 19-2-2021 Swati D10

Therefore, EF = (2 × AD × BC)/(AD + BC)

⇒ (2 × 20 × 5) /(20 + 5)

⇒ 200/25

⇒ 8 cm

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