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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:
  • a)
    8 cm
  • b)
    12 cm
  • c)
    10 cm
  • d)
    15 cm
  • e)
    13 cm
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
In trapezium ABCD, AD‖BC, O is intersection point of diagonals BD and...
Given
AD //BC
BC = 5 cm and AD = 20 cm
We know that.
Therefore,
⇒ 200/25
⇒ 8 cm
Hence, the correct option is (A).
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Most Upvoted Answer
In trapezium ABCD, AD‖BC, O is intersection point of diagonals BD and...
Given Information:
- Trapezium ABCD with AD || BC
- O is the intersection point of diagonals BD and AC
- Points F and E are on AB and CD respectively, such that FE passes through point O
- BC = 5 cm and AD = 20 cm

To find:
The length of EF.

Solution:
1. Since AD || BC, triangle BOC is similar to triangle AOD (by AA similarity).
2. Let x be the length of BE and y be the length of CF.
3. Using the similarity of triangles BOC and AOD, we have the following ratios:
- BO/OC = AO/OD
- BC/OC = AD/OD
4. Substituting the given values, we get:
- 5/x = 20/y
- x/y = 5/20
- x/y = 1/4
- x = (1/4)y
5. We can also find the ratio of the areas of triangles BOC and AOD:
- Area of BOC/Area of AOD = (BO/OC)^2 = (BC/AD)^2 = (5/20)^2
- (BO/OC)^2 = 1/16
- BO/OC = 1/4
- BO = (1/4)OC
6. Since FE passes through point O, triangles BFO and CEO are similar (by AA similarity).
7. Using the similarity of triangles BFO and CEO, we have the following ratios:
- BF/EO = BO/OC
- BF/EO = (1/4)OC/OC
- BF/EO = 1/4
- BF = (1/4)EO
8. The length of EF is given by EF = BE + BF + EO.
9. Substituting the values we found earlier, we get:
- EF = x + (1/4)EO + EO
- EF = x + (5/4)EO
- EF = (1/4)y + (5/4)EO
10. Since BE + EO + EO = BC, we have x + EO + EO = 5.
11. Substituting this in the equation for EF, we get:
- EF = (1/4)y + (5/4)(5 - EO)
- EF = (1/4)y + (25/4) - (5/4)EO
12. Since BF/EO = 1/4, we have BF = (1/4)EO.
13. Substituting this in the equation for EF, we get:
- EF = (1/4)y + (25/4) - (5/4)(4BF)
- EF = (1/4)y + (25/4) - 5BF
- EF = (1/4)y + (25/4) - 5(1/4)EO
- EF = (1/4)y + (25/4) - (5/4)EO
- EF = (1/4)y + (25/4) - (5/4)(1/4)y
- EF = (1/4)y + (25/4) - (
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Directions for Questions: The figure below shows the street map for a certain region with the street intersections marked from a through l. A person standing at an intersection can see along straight lines to other intersections that are in her line of sight and all other people standing at these intersections. For example, a person standing at intersection g can see all people standing at intersections b, c, e, f, h, and k. In particular, the person standing at intersection g can see the person standing at intersection e irrespective of whether there is a person standing at intersection f.Six people U, V, W, X, Y, and Z, are standing at different intersections. No two people are standing at the same intersection.The following additional facts are known.1. X, U, and Z are standing at the three corners of a triangle formed by three street segments.2. X can see only U and Z.3. Y can see only U and W.4. U sees V standing in the next intersection behind Z.5. W cannot see V or Z.6. No one among the six is standing at intersection d.(2019)Q. Who can V see?

The figure below shows the street map for a certain region with the street intersections marked from a through l. A person standing at an intersection can see along straight lines to other intersections that are in her line of sight and all other people standing at these intersections. For example, a person standing at intersection g can see all people standing at intersections b, c, e, f, h, and k. In particular, the person standing at intersection g can see the person standing at intersection e irrespective of whether there is a person standing at intersection f.Six people U, V, W, X, Y, and Z, are standing at different intersections. No two people are standing at the same intersection.The following additional facts are known. 1. X, U, and Z are standing at the three corners of a triangle formed by three street segments. 2. X can see only U and Z. 3. Y can see only U and W. 4. U sees V standing in the next intersection behind Z.5. W cannot see V or Z. 6. No one among the six is standing at intersection d.Q. Who is standing at intersection a?

InstructionsComprehension:The figure below shows the street map for a certain region with the street intersections marked from a through l. A person standing at an intersection can see along straight lines to other intersections that are in her line of sight and all other people standing at these intersections. For example, a person standing at intersection g can see all people standing at intersections b, c, e, f, h, and k. In particular, the person standing at intersection g can see the person standing at intersection e irrespective of whether there is a person standing at intersection f.Six people U, V, W, X, Y, and Z, are standing at different intersections. No two people are standing at the same intersection.The following additional facts are known.1. X, U, and Z are standing at the three corners of a triangle formed by three street segments.2. X can see only U and Z.3. Y can see only U and W.4. U sees V standing in the next intersection behind Z.5. W cannot see V or Z.6. No one among the six is standing at intersection d.Q.Who is standing at intersection a?

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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:a)8 cmb)12 cmc)10 cmd)15 cme)13 cmCorrect answer is option 'A'. Can you explain this answer?
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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:a)8 cmb)12 cmc)10 cmd)15 cme)13 cmCorrect answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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:a)8 cmb)12 cmc)10 cmd)15 cme)13 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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:a)8 cmb)12 cmc)10 cmd)15 cme)13 cmCorrect answer is option 'A'. Can you explain this answer?.
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