Class 10 Exam > Class 10 Questions > In trapezium ABCD a line EF cuts the diagonal...
Start Learning for Free
In trapezium ABCD a line EF cuts the diagonal AC in O such that AO/OC = 2/3 and EF is parallel to BC.In what ratio does EF cut AB and CD?
- a)1:2
- b)3:4
- c)2:3
- d)1:4
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
In trapezium ABCD a line EF cuts the diagonal AC in O such that AO/OC ...
Solution:
Given that,
AO/OC = 2/3 and EF is parallel to BC
We have to find the ratio in which EF cuts AB and CD.
Let's join E and C and extend it to meet AB at G.
Now, we have two similar triangles AOG and COE.
By the property of similar triangles,
AO/OC = AG/CE = 2/3
If we take CG as x, then AG will be (2/3)x and CE will be (1/3)x.
Now, let's join E and F and extend it to meet DC at H.
By the property of parallel lines,
∠DBC = ∠FEH (Alternate angles)
Also, ∠BDC = ∠HEF (Alternate angles)
Therefore, ΔBDC ~ ΔFEH (By AA similarity)
By the property of similar triangles,
DC/FE = BC/EF
DC/(DC + EF) = BC/EF
DC/BC = EF/(DC + EF)
DC/BC = EF/BD
DC/BC = EF/(BC + CD)
BC/CD = EF/DC
CD/BC = DC/EF
Let's assume EF cuts AB at G1 and CD at H1.
Now, let's take BC/CD as x. Then, CD = x and BC = 1.
Therefore, DC = x + 1.
From the above equation, we get
CD/BC = DC/EF
x/(1) = (x + 1)/EF
EF = (x + 1)/x
Now, let's consider the triangle AEF.
By the property of similar triangles,
AG1/GE = AO/OE (From ΔAOG and ΔEOC)
AG1/(EF - x) = 2/3 (As AO/OC = 2/3)
AG1 = (2/3)(EF - x)
Similarly, let's consider the triangle DEH.
By the property of similar triangles,
DH1/HE = DC/CE (From ΔDCB and ΔEFC)
DH1/(EF - x) = x/3
DH1 = (x/3)(EF - x)
Now, let's find the ratio in which EF cuts AB and CD.
Ratio = AG1/DH1
= [(2/3)(EF - x)]/[(x/3)(EF - x)]
= 2x/3x
= 2:3
Therefore, the ratio in which EF cuts AB and CD is 2:3.
Hence, the correct option is (C).
Given that,
AO/OC = 2/3 and EF is parallel to BC
We have to find the ratio in which EF cuts AB and CD.
Let's join E and C and extend it to meet AB at G.
Now, we have two similar triangles AOG and COE.
By the property of similar triangles,
AO/OC = AG/CE = 2/3
If we take CG as x, then AG will be (2/3)x and CE will be (1/3)x.
Now, let's join E and F and extend it to meet DC at H.
By the property of parallel lines,
∠DBC = ∠FEH (Alternate angles)
Also, ∠BDC = ∠HEF (Alternate angles)
Therefore, ΔBDC ~ ΔFEH (By AA similarity)
By the property of similar triangles,
DC/FE = BC/EF
DC/(DC + EF) = BC/EF
DC/BC = EF/(DC + EF)
DC/BC = EF/BD
DC/BC = EF/(BC + CD)
BC/CD = EF/DC
CD/BC = DC/EF
Let's assume EF cuts AB at G1 and CD at H1.
Now, let's take BC/CD as x. Then, CD = x and BC = 1.
Therefore, DC = x + 1.
From the above equation, we get
CD/BC = DC/EF
x/(1) = (x + 1)/EF
EF = (x + 1)/x
Now, let's consider the triangle AEF.
By the property of similar triangles,
AG1/GE = AO/OE (From ΔAOG and ΔEOC)
AG1/(EF - x) = 2/3 (As AO/OC = 2/3)
AG1 = (2/3)(EF - x)
Similarly, let's consider the triangle DEH.
By the property of similar triangles,
DH1/HE = DC/CE (From ΔDCB and ΔEFC)
DH1/(EF - x) = x/3
DH1 = (x/3)(EF - x)
Now, let's find the ratio in which EF cuts AB and CD.
Ratio = AG1/DH1
= [(2/3)(EF - x)]/[(x/3)(EF - x)]
= 2x/3x
= 2:3
Therefore, the ratio in which EF cuts AB and CD is 2:3.
Hence, the correct option is (C).
Free Test
FREE
| Start Free Test |
Community Answer
In trapezium ABCD a line EF cuts the diagonal AC in O such that AO/OC ...
By bpt theorem ration of both are same
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
In trapezium ABCD a line EF cuts the diagonal AC in O such that AO/OC = 2/3and EF is parallel to BC.In what ratio does EF cut AB and CD?a)1:2b)3:4c)2:3d)1:4Correct answer is option 'C'. Can you explain this answer?
Question Description
In trapezium ABCD a line EF cuts the diagonal AC in O such that AO/OC = 2/3and EF is parallel to BC.In what ratio does EF cut AB and CD?a)1:2b)3:4c)2:3d)1:4Correct answer is option 'C'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about In trapezium ABCD a line EF cuts the diagonal AC in O such that AO/OC = 2/3and EF is parallel to BC.In what ratio does EF cut AB and CD?a)1:2b)3:4c)2:3d)1:4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In trapezium ABCD a line EF cuts the diagonal AC in O such that AO/OC = 2/3and EF is parallel to BC.In what ratio does EF cut AB and CD?a)1:2b)3:4c)2:3d)1:4Correct answer is option 'C'. Can you explain this answer?.
In trapezium ABCD a line EF cuts the diagonal AC in O such that AO/OC = 2/3and EF is parallel to BC.In what ratio does EF cut AB and CD?a)1:2b)3:4c)2:3d)1:4Correct answer is option 'C'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about In trapezium ABCD a line EF cuts the diagonal AC in O such that AO/OC = 2/3and EF is parallel to BC.In what ratio does EF cut AB and CD?a)1:2b)3:4c)2:3d)1:4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In trapezium ABCD a line EF cuts the diagonal AC in O such that AO/OC = 2/3and EF is parallel to BC.In what ratio does EF cut AB and CD?a)1:2b)3:4c)2:3d)1:4Correct answer is option 'C'. Can you explain this answer?.
Solutions for In trapezium ABCD a line EF cuts the diagonal AC in O such that AO/OC = 2/3and EF is parallel to BC.In what ratio does EF cut AB and CD?a)1:2b)3:4c)2:3d)1:4Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of In trapezium ABCD a line EF cuts the diagonal AC in O such that AO/OC = 2/3and EF is parallel to BC.In what ratio does EF cut AB and CD?a)1:2b)3:4c)2:3d)1:4Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In trapezium ABCD a line EF cuts the diagonal AC in O such that AO/OC = 2/3and EF is parallel to BC.In what ratio does EF cut AB and CD?a)1:2b)3:4c)2:3d)1:4Correct answer is option 'C'. Can you explain this answer?, a detailed solution for In trapezium ABCD a line EF cuts the diagonal AC in O such that AO/OC = 2/3and EF is parallel to BC.In what ratio does EF cut AB and CD?a)1:2b)3:4c)2:3d)1:4Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of In trapezium ABCD a line EF cuts the diagonal AC in O such that AO/OC = 2/3and EF is parallel to BC.In what ratio does EF cut AB and CD?a)1:2b)3:4c)2:3d)1:4Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In trapezium ABCD a line EF cuts the diagonal AC in O such that AO/OC = 2/3and EF is parallel to BC.In what ratio does EF cut AB and CD?a)1:2b)3:4c)2:3d)1:4Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup