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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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In trapezium ABCD, AD‖BC, O is intersection point of diagonals BD and...
Given
View all questions of this test
AD //BC
BC = 5 cm and AD = 20 cm
We know that.
Therefore,
⇒ 200/25
⇒ 8 cm
Hence, the correct option is (A).
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) - (
- 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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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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